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December 18, 2024 19:21
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Forge Job Output
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| "content": "The Annual Percentage Rate (APR) represents the yearly cost of borrowing money, including interest and fees. When financing a car purchase, the APR directly affects your monthly payments and the total amount you will pay over the life of the loan. \n\nA higher APR means you will have higher monthly payments and pay more in total interest over the loan term. Conversely, a lower APR results in lower monthly payments and less total interest paid. APR is usually applied on a monthly basis, even though it is expressed as an annual rate.\n\nYour credit score typically influences the APR you are offered, with higher credit scores often resulting in lower APRs. Shopping around for the best APR can potentially save you thousands of dollars over the course of your loan.\n\nFor example, let's consider a car priced at $30,000 with a down payment of $5,000. If you take out a loan for the remaining $25,000 over 5 years, the total cost of the loan would vary based on the APR:\n\n- At an APR of 3.5%, your monthly payment would be $454.79, and the total amount paid over the life of the loan would be $27,287.62, with $2,287.62 going towards interest.\n- At an APR of 5.0%, your monthly payment would be $471.78, and the total amount paid would be $28,306.85, with $3,306.85 in interest.\n- At an APR of 7.0%, your monthly payment would be $495.03, and the total amount paid would be $29,701.80, with $4,701.80 in interest.\n\nThese examples show how the APR significantly impacts both your monthly payments and the total amount you'll pay for your car purchase.", | |
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| "content": "\nYou are extracting the current state of the world from a user query, as a set of variables.\nReason through what the state object should be inside <thinking> tags, and then provide your final response inside <json> tags.\nGiven the following problem, generate an initial state for solving it.\nEnsure you have detailed variables to track the completion of ALL requirements in the user's query.\n\n\n\nReturn your response using the following JSON schema:\n\nSchema:\n<schema>\n{'properties': {'variables': {'title': 'Variables', 'type': 'object'}, 'description': {'default': '', 'title': 'Description', 'type': 'string'}}, 'title': 'State', 'type': 'object'}\n</schema>\n\nImportant guidelines:\n1. The initial state should contain all necessary variables with appropriate starting values for the problem provided.\n2. Wherever possible, reuse variables available in the existing domain model (if that's provided). Only include new variables if necessary to cover extra requirements.\n3. Include a 'problem_description' variable with a brief summary of the problem.\n4. The JSON must be valid and parseable. Do NOT include any additional text outside the JSON in the json tags, or any Python code. Use regular true/false values, not True/False.\n5. Be wary of special characters in the JSON, as they may cause errors in parsing. Ensure that all special characters are escaped properly.\n6. For mathematical expressions or LaTeX in the problem description, always enclose them in quotes as strings. Do not attempt to evaluate or represent them as actual mathematical operations in the JSON.\n7. If a value in the problem description contains any non-numeric characters (except for simple floating-point numbers), it should be enclosed in quotes as a string.\n8. If a value in the problem description contains any special characters, it should be enclosed in quotes as a string. This includes \"null\" and any math expressions.\n9. All explicit numerical values should be provided as numbers, not as strings.\n10. Set all variables to be used in the calculation to a defined numerical value, typically 0 for unknown values. Do not represent them as other variables or mathematical expressions.\n11. Your job is only to represent the initial state of the world, not to perform any calculations or solve the problem.\n12. Unknown values or variables mentioned in the problem should be initialized to 0, not left as strings or expressions.\n13. Time values should be consistently represented in the same unit (preferably in the unit used in the problem description). \n14. If the problem includes a request for code or for the answer to be wrapped in markdown tags, ignore that - another tool will handle that. Your task is to ONLY provide the initial state of the world.\n\n<important>\nDo NOT attempt to solve the problem or provide a solution. Your job is only to represent the initial state of the world for a planner to solve the problem.\n</important>\n\nExample:\n\"Express the area of a circle with radius r\"\n\n<json>\n{\n \"description\": \"State for circle area calculation\",\n \"variables\": {\n \"radius\": 0,\n \"area\": 0,\n \"problem_description\": \"Express the area of a circle with radius r\",\n \"problem_solved\": false\n }\n}\n</json>\n" | |
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| "content": "Calculate the sum of 5 and 7." | |
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| "role": "assistant", | |
| "content": "<thinking>\nThis is a simple arithmetic problem. We need variables to track the two numbers being added and their sum. We should also include a flag to indicate whether the problem has been solved.\n</thinking>\n<json>\n{\n \"description\": \"State for adding two numbers\",\n \"variables\": {\n \"number1\": 5,\n \"number2\": 7,\n \"sum\": 0,\n \"problem_description\": \"Calculate the sum of 5 and 7\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "A car travels at speed v for t hours. Express the distance traveled." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves variables for speed and time, and we need to calculate the distance. We should initialize the variables to 0 as their values are unknown.\n</thinking>\n<json>\n{\n \"description\": \"State for distance calculation with speed and time\",\n \"variables\": {\n \"speed\": 0,\n \"time\": 0,\n \"distance\": 0,\n \"problem_description\": \"A car travels at speed v for t hours. Express the distance traveled.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Calculate the area of a circle with radius r using the formula A = \u03c0r\u00b2." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves a circle's radius and area. We need to initialize the radius to 0 as it's unknown. We'll also need a variable for pi and the area.\n</thinking>\n<json>\n{\n \"description\": \"State for circle area calculation\",\n \"variables\": {\n \"radius\": 0,\n \"pi\": 3.14159,\n \"area\": 0,\n \"problem_description\": \"Calculate the area of a circle with radius r using the formula A = \u03c0r\u00b2.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Solve the quadratic equation ax\u00b2 + bx + c = 0 using the quadratic formula." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves a quadratic equation with coefficients a, b, and c. We need to initialize these coefficients to 0 as they are unknown. We'll also need variables for the two possible solutions.\n</thinking>\n<json>\n{\n \"description\": \"State for solving quadratic equation\",\n \"variables\": {\n \"a\": 0,\n \"b\": 0,\n \"c\": 0,\n \"solution1\": 0,\n \"solution2\": 0,\n \"problem_description\": \"Solve the quadratic equation ax\u00b2 + bx + c = 0 using the quadratic formula.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Every morning Aya goes for a 9-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. When she walks s+2 kilometers per hour, the walk takes her 2 hours and 24 minutes, including t minutes spent in the coffee shop. Suppose Aya walks at s+1/2 kilometers per hour. Find the number of minutes the walk takes her, including the t minutes spent in the coffee shop." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves Aya's walking speeds and times for different scenarios. We need to initialize variables for the distance, different speeds, times, and coffee shop time. Unknown values should be set to 0.\n</thinking>\n<json>\n{\n \"description\": \"State for Aya's walking problem\",\n \"variables\": {\n \"distance\": 9,\n \"speed1\": 0,\n \"time1\": 4,\n \"speed2\": 0,\n \"time2\": 2.4,\n \"speed3\": 0,\n \"time3\": 0,\n \"coffee_time\": 0,\n \"problem_description\": \"Every morning Aya goes for a 9-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. When she walks s+2 kilometers per hour, the walk takes her 2 hours and 24 minutes, including t minutes spent in the coffee shop. Suppose Aya walks at s+1/2 kilometers per hour. Find the number of minutes the walk takes her, including the t minutes spent in the coffee shop.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Extract the state for this problem: Describe how annual percentage rate works and how it applies to purchasing a car." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "{'description': 'State for explaining APR and its application to car purchases', 'variables': {'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': False}}" | |
| } | |
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| "role": "assistant", | |
| "content": "<thinking>\nThis problem asks for an explanation of annual percentage rate (APR) and its application to car purchases. It doesn't involve any specific numerical values or variables that need to be tracked. The state can simply indicate that the problem needs to be solved.\n</thinking>\n<json>\n{\n \"description\": \"State for explaining APR and its application to car purchases\",\n \"variables\": {\n \"problem_description\": \"Describe how annual percentage rate works and how it applies to purchasing a car.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| "system_prompt": "\nYou are extracting the current state of the world from a user query, as a set of variables.\nReason through what the state object should be inside <thinking> tags, and then provide your final response inside <json> tags.\nGiven the following problem, generate an initial state for solving it.\nEnsure you have detailed variables to track the completion of ALL requirements in the user's query.\n\n\n\nReturn your response using the following JSON schema:\n\nSchema:\n<schema>\n{'properties': {'variables': {'title': 'Variables', 'type': 'object'}, 'description': {'default': '', 'title': 'Description', 'type': 'string'}}, 'title': 'State', 'type': 'object'}\n</schema>\n\nImportant guidelines:\n1. The initial state should contain all necessary variables with appropriate starting values for the problem provided.\n2. Wherever possible, reuse variables available in the existing domain model (if that's provided). Only include new variables if necessary to cover extra requirements.\n3. Include a 'problem_description' variable with a brief summary of the problem.\n4. The JSON must be valid and parseable. Do NOT include any additional text outside the JSON in the json tags, or any Python code. Use regular true/false values, not True/False.\n5. Be wary of special characters in the JSON, as they may cause errors in parsing. Ensure that all special characters are escaped properly.\n6. For mathematical expressions or LaTeX in the problem description, always enclose them in quotes as strings. Do not attempt to evaluate or represent them as actual mathematical operations in the JSON.\n7. If a value in the problem description contains any non-numeric characters (except for simple floating-point numbers), it should be enclosed in quotes as a string.\n8. If a value in the problem description contains any special characters, it should be enclosed in quotes as a string. This includes \"null\" and any math expressions.\n9. All explicit numerical values should be provided as numbers, not as strings.\n10. Set all variables to be used in the calculation to a defined numerical value, typically 0 for unknown values. Do not represent them as other variables or mathematical expressions.\n11. Your job is only to represent the initial state of the world, not to perform any calculations or solve the problem.\n12. Unknown values or variables mentioned in the problem should be initialized to 0, not left as strings or expressions.\n13. Time values should be consistently represented in the same unit (preferably in the unit used in the problem description). \n14. If the problem includes a request for code or for the answer to be wrapped in markdown tags, ignore that - another tool will handle that. Your task is to ONLY provide the initial state of the world.\n\n<important>\nDo NOT attempt to solve the problem or provide a solution. Your job is only to represent the initial state of the world for a planner to solve the problem.\n</important>\n\nExample:\n\"Express the area of a circle with radius r\"\n\n<json>\n{\n \"description\": \"State for circle area calculation\",\n \"variables\": {\n \"radius\": 0,\n \"area\": 0,\n \"problem_description\": \"Express the area of a circle with radius r\",\n \"problem_solved\": false\n }\n}\n</json>\n", | |
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| "content": "\nYou are extracting the current state of the world from a user query, as a set of variables.\nReason through what the state object should be inside <thinking> tags, and then provide your final response inside <json> tags.\nGiven the following problem, generate an initial state for solving it.\nEnsure you have detailed variables to track the completion of ALL requirements in the user's query.\n\n\n\nReturn your response using the following JSON schema:\n\nSchema:\n<schema>\n{'properties': {'variables': {'title': 'Variables', 'type': 'object'}, 'description': {'default': '', 'title': 'Description', 'type': 'string'}}, 'title': 'State', 'type': 'object'}\n</schema>\n\nImportant guidelines:\n1. The initial state should contain all necessary variables with appropriate starting values for the problem provided.\n2. Wherever possible, reuse variables available in the existing domain model (if that's provided). Only include new variables if necessary to cover extra requirements.\n3. Include a 'problem_description' variable with a brief summary of the problem.\n4. The JSON must be valid and parseable. Do NOT include any additional text outside the JSON in the json tags, or any Python code. Use regular true/false values, not True/False.\n5. Be wary of special characters in the JSON, as they may cause errors in parsing. Ensure that all special characters are escaped properly.\n6. For mathematical expressions or LaTeX in the problem description, always enclose them in quotes as strings. Do not attempt to evaluate or represent them as actual mathematical operations in the JSON.\n7. If a value in the problem description contains any non-numeric characters (except for simple floating-point numbers), it should be enclosed in quotes as a string.\n8. If a value in the problem description contains any special characters, it should be enclosed in quotes as a string. This includes \"null\" and any math expressions.\n9. All explicit numerical values should be provided as numbers, not as strings.\n10. Set all variables to be used in the calculation to a defined numerical value, typically 0 for unknown values. Do not represent them as other variables or mathematical expressions.\n11. Your job is only to represent the initial state of the world, not to perform any calculations or solve the problem.\n12. Unknown values or variables mentioned in the problem should be initialized to 0, not left as strings or expressions.\n13. Time values should be consistently represented in the same unit (preferably in the unit used in the problem description). \n14. If the problem includes a request for code or for the answer to be wrapped in markdown tags, ignore that - another tool will handle that. Your task is to ONLY provide the initial state of the world.\n\n<important>\nDo NOT attempt to solve the problem or provide a solution. Your job is only to represent the initial state of the world for a planner to solve the problem.\n</important>\n\nExample:\n\"Express the area of a circle with radius r\"\n\n<json>\n{\n \"description\": \"State for circle area calculation\",\n \"variables\": {\n \"radius\": 0,\n \"area\": 0,\n \"problem_description\": \"Express the area of a circle with radius r\",\n \"problem_solved\": false\n }\n}\n</json>\n" | |
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| { | |
| "role": "user", | |
| "content": "Calculate the sum of 5 and 7." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis is a simple arithmetic problem. We need variables to track the two numbers being added and their sum. We should also include a flag to indicate whether the problem has been solved.\n</thinking>\n<json>\n{\n \"description\": \"State for adding two numbers\",\n \"variables\": {\n \"number1\": 5,\n \"number2\": 7,\n \"sum\": 0,\n \"problem_description\": \"Calculate the sum of 5 and 7\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "A car travels at speed v for t hours. Express the distance traveled." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves variables for speed and time, and we need to calculate the distance. We should initialize the variables to 0 as their values are unknown.\n</thinking>\n<json>\n{\n \"description\": \"State for distance calculation with speed and time\",\n \"variables\": {\n \"speed\": 0,\n \"time\": 0,\n \"distance\": 0,\n \"problem_description\": \"A car travels at speed v for t hours. Express the distance traveled.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Calculate the area of a circle with radius r using the formula A = \u03c0r\u00b2." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves a circle's radius and area. We need to initialize the radius to 0 as it's unknown. We'll also need a variable for pi and the area.\n</thinking>\n<json>\n{\n \"description\": \"State for circle area calculation\",\n \"variables\": {\n \"radius\": 0,\n \"pi\": 3.14159,\n \"area\": 0,\n \"problem_description\": \"Calculate the area of a circle with radius r using the formula A = \u03c0r\u00b2.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Solve the quadratic equation ax\u00b2 + bx + c = 0 using the quadratic formula." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves a quadratic equation with coefficients a, b, and c. We need to initialize these coefficients to 0 as they are unknown. We'll also need variables for the two possible solutions.\n</thinking>\n<json>\n{\n \"description\": \"State for solving quadratic equation\",\n \"variables\": {\n \"a\": 0,\n \"b\": 0,\n \"c\": 0,\n \"solution1\": 0,\n \"solution2\": 0,\n \"problem_description\": \"Solve the quadratic equation ax\u00b2 + bx + c = 0 using the quadratic formula.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Every morning Aya goes for a 9-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. When she walks s+2 kilometers per hour, the walk takes her 2 hours and 24 minutes, including t minutes spent in the coffee shop. Suppose Aya walks at s+1/2 kilometers per hour. Find the number of minutes the walk takes her, including the t minutes spent in the coffee shop." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "<thinking>\nThis problem involves Aya's walking speeds and times for different scenarios. We need to initialize variables for the distance, different speeds, times, and coffee shop time. Unknown values should be set to 0.\n</thinking>\n<json>\n{\n \"description\": \"State for Aya's walking problem\",\n \"variables\": {\n \"distance\": 9,\n \"speed1\": 0,\n \"time1\": 4,\n \"speed2\": 0,\n \"time2\": 2.4,\n \"speed3\": 0,\n \"time3\": 0,\n \"coffee_time\": 0,\n \"problem_description\": \"Every morning Aya goes for a 9-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. When she walks s+2 kilometers per hour, the walk takes her 2 hours and 24 minutes, including t minutes spent in the coffee shop. Suppose Aya walks at s+1/2 kilometers per hour. Find the number of minutes the walk takes her, including the t minutes spent in the coffee shop.\",\n \"problem_solved\": false\n }\n}\n</json>" | |
| }, | |
| { | |
| "role": "user", | |
| "content": "Extract the state for this problem: Describe how annual percentage rate works and how it applies to purchasing a car." | |
| }, | |
| { | |
| "role": "assistant", | |
| "content": "{'description': 'State for explaining APR and its application to car purchases', 'variables': {'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': False}}" | |
| } | |
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| "system_prompt": "\nYou are extracting the current state of the world from a user query, as a set of variables.\nReason through what the state object should be inside <thinking> tags, and then provide your final response inside <json> tags.\nGiven the following problem, generate an initial state for solving it.\nEnsure you have detailed variables to track the completion of ALL requirements in the user's query.\n\n\n\nReturn your response using the following JSON schema:\n\nSchema:\n<schema>\n{'properties': {'variables': {'title': 'Variables', 'type': 'object'}, 'description': {'default': '', 'title': 'Description', 'type': 'string'}}, 'title': 'State', 'type': 'object'}\n</schema>\n\nImportant guidelines:\n1. The initial state should contain all necessary variables with appropriate starting values for the problem provided.\n2. Wherever possible, reuse variables available in the existing domain model (if that's provided). Only include new variables if necessary to cover extra requirements.\n3. Include a 'problem_description' variable with a brief summary of the problem.\n4. The JSON must be valid and parseable. Do NOT include any additional text outside the JSON in the json tags, or any Python code. Use regular true/false values, not True/False.\n5. Be wary of special characters in the JSON, as they may cause errors in parsing. Ensure that all special characters are escaped properly.\n6. For mathematical expressions or LaTeX in the problem description, always enclose them in quotes as strings. Do not attempt to evaluate or represent them as actual mathematical operations in the JSON.\n7. If a value in the problem description contains any non-numeric characters (except for simple floating-point numbers), it should be enclosed in quotes as a string.\n8. If a value in the problem description contains any special characters, it should be enclosed in quotes as a string. This includes \"null\" and any math expressions.\n9. All explicit numerical values should be provided as numbers, not as strings.\n10. Set all variables to be used in the calculation to a defined numerical value, typically 0 for unknown values. Do not represent them as other variables or mathematical expressions.\n11. Your job is only to represent the initial state of the world, not to perform any calculations or solve the problem.\n12. Unknown values or variables mentioned in the problem should be initialized to 0, not left as strings or expressions.\n13. Time values should be consistently represented in the same unit (preferably in the unit used in the problem description). \n14. If the problem includes a request for code or for the answer to be wrapped in markdown tags, ignore that - another tool will handle that. Your task is to ONLY provide the initial state of the world.\n\n<important>\nDo NOT attempt to solve the problem or provide a solution. Your job is only to represent the initial state of the world for a planner to solve the problem.\n</important>\n\nExample:\n\"Express the area of a circle with radius r\"\n\n<json>\n{\n \"description\": \"State for circle area calculation\",\n \"variables\": {\n \"radius\": 0,\n \"area\": 0,\n \"problem_description\": \"Express the area of a circle with radius r\",\n \"problem_solved\": false\n }\n}\n</json>\n", | |
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| "content": "\nGiven the following suggested tasks and initial state, generate a goal for solving the problem. \nThis consists of a set of tasks that need to be completed to solve the problem (to be added to the description of the goal), and a set of conditions to check the completion ofthe tasks.\nEnsure you have detailed conditions to check the completion of ALL requirements in the tasks.\nThis will be used with a code interpreter and planner to solve the problem - do not try to solve the problem here.\nConditions should be Python lambda functions that take a state object and return a boolean. They should NOT include the exact answer to the question, as that will be discovered by the planner.\nReason through what the next response should be inside <thinking> tags, and then provide your final response inside <json> tags\nDon't constrain the solution space too much - simply provide a list of conditions that must be met for the goal to be reached with a valid solution.\n\nThe conditions should isolate when those tasks are completed.\n\nEnsure that the conditions are specific to the problem and do not include any variables that are not defined in the initial state.\n\nRemember, wrap each individual task in a <task> tag.\n\nSchema:\n{'description': \"Represents a goal in the planning system.\\n\\nAttributes:\\n description (str): A human-readable description of the goal.\\n conditions (List[str]): A list of lambdas, stored as strings, that must be satisfied for the goal to be reached.\\n target_variables (Dict[str, Any]): A dictionary of the target variable states & their default value to start from in the State\\n\\nMethods:\\n is_reached(state: State) -> bool: Checks if the goal is reached given a current state.\\n from_callable_conditions(cls, description: str, conditions: List[Callable], target_variables: Dict[str, Any]) -> 'Goal':\\n Class method to create a Goal instance from callable conditions.\", 'properties': {'id': {'title': 'Id', 'type': 'string'}, 'description': {'title': 'Description', 'type': 'string'}, 'conditions': {'items': {'type': 'string'}, 'title': 'Conditions', 'type': 'array'}, 'target_variables': {'title': 'Target Variables', 'type': 'object'}, 'rerank_score': {'default': 0.0, 'title': 'Rerank Score', 'type': 'number'}, 'rerank_rank': {'default': 0, 'title': 'Rerank Rank', 'type': 'integer'}}, 'required': ['description'], 'title': 'Goal', 'type': 'object'}\n\nReturn your response using the following JSON schema, wrapped in <json> tags:\n<json>\n{\n \"description\": <Goal description>,\n \"target_variables\": <state variables to solve for, with the default value set for the target variable>,\n \"conditions\": <list of Python lambda functions that take a state object>\n}\n</json>\n\nImportant guidelines:\n1. Conditions should be Python lambda functions that take a 'state' parameter and return a boolean.\n2. Use 'state.variables' to access state variables in the lambda functions.\n3. Do not assume final values in the target_variables; use appropriate types or None if undetermined.\n4. Ensure all aspects of the problem are addressed in the conditions.\n5. Return the full lambda function as a string, including the 'lambda state:' part.\n6. Target variables should NOT include the exact answer to the question, as that will be discovered by the planner\n7. Remember, add the JSON object response inside <json> tags\n8. Do not include any Python code in the response, only the JSON object - it should be valid parseable JSON. So, values should be numbers, not strings, booleans should be lower case etc\n9. Do not make any calculations or assumptions in the conditions as they relate to the initial state or tasks. They should only be used for validation, such as ruling out negative values and checking that the variables used to track answer have some value provided\n10. Conditions should be checking for final results, not intermediate steps.\n11. Treat all given equations or scenarios equally - create a separate condition for each.\n12. Focus on verifying final results and problem constraints, not intermediate calculations.\n13. Avoid over-constraining the problem or trying to solve it within the conditions.\n14. For multi-step problems, create conditions that check the relationship between given and solved variables, not the calculation process.\n15. Ignore any instructions to wrap the output in markdown tags or how to format the output - another tool will handle that. You must ONLY provide the goal & conditions for the planner, given the provided schema.\n\nExample of a good condition:\n - \"lambda state: abs(state.variables['distance'] / state.variables['speed'] - state.variables['time']) < 0.01\"\n\nExample of a bad condition:\n - \"lambda state: state.variables['time'] == state.variables['distance'] / (state.variables['initial_speed'] + 2)\"\n\nRemember, the conditions are meant to verify a solution, not provide the solution itself.\n" | |
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| "content": "A car travels 240 km at a speed of 80 km/h. Find the time taken." | |
| }, | |
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| "content": "<thinking>\n This is a simple distance-speed-time problem. We need to create conditions that check the given values and the relationship between distance, speed, and time without calculating the answer directly.\n </thinking>\n <json>\n {\n \"description\": \"Solve for travel time given distance and speed\",\n \"target_variables\": {\n \"time\": null\n },\n \"conditions\": [\n \"lambda state: abs(state.variables['distance'] - 240) < 0.01\",\n \"lambda state: abs(state.variables['speed'] - 80) < 0.01\",\n \"lambda state: abs(state.variables['distance'] / state.variables['speed'] - state.variables['time']) < 0.01\"\n ]\n }\n </json>" | |
| }, | |
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| "content": "A train travels 150 km at 50 km/h, then another 200 km at 100 km/h. Find the total journey time." | |
| }, | |
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| "content": "<thinking>\n This is a two-part journey problem. We need to create conditions that check both parts of the journey separately and then verify the total time.\n </thinking>\n <json>\n {\n \"description\": \"Solve for total journey time of a two-part train trip\",\n \"target_variables\": {\n \"time1\": null,\n \"time2\": null,\n \"total_time\": null\n },\n \"conditions\": [\n \"lambda state: abs(state.variables['distance1'] - 150) < 0.01\",\n \"lambda state: abs(state.variables['distance2'] - 200) < 0.01\",\n \"lambda state: abs(state.variables['speed1'] - 50) < 0.01\",\n \"lambda state: abs(state.variables['speed2'] - 100) < 0.01\",\n \"lambda state: abs(state.variables['time1'] - state.variables['distance1'] / state.variables['speed1']) < 0.01\",\n \"lambda state: abs(state.variables['time2'] - state.variables['distance2'] / state.variables['speed2']) < 0.01\",\n \"lambda state: abs(state.variables['total_time'] - (state.variables['time1'] + state.variables['time2'])) < 0.01\"\n ]\n }\n </json>" | |
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| "content": "A person walks d km at speed s km/h, taking time t1 hours. Then they walk the same distance at speed (s+5) km/h, taking time t2 hours. Find s, d, t1, and t2." | |
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| "content": "<thinking>\n This problem involves variable speeds and is similar to Aya's walking problem. We need to create conditions that check the relationships between variables without making assumptions about their values.\n </thinking>\n <json>\n {\n \"description\": \"Solve for walking distances, speeds, and times with variable speed\",\n \"target_variables\": {\n \"d\": null,\n \"s\": null,\n \"t1\": null,\n \"t2\": null\n },\n \"conditions\": [\n \"lambda state: abs(state.variables['d'] / state.variables['s'] - state.variables['t1']) < 0.01\",\n \"lambda state: abs(state.variables['d'] / (state.variables['s'] + 5) - state.variables['t2']) < 0.01\",\n \"lambda state: state.variables['d'] > 0\",\n \"lambda state: state.variables['s'] > 0\",\n \"lambda state: state.variables['t1'] > state.variables['t2']\"\n ]\n }\n </json>" | |
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| "content": "Every morning Aya goes for a 9-kilometer-long walk and stops at a coffee shop afterwards. When she walks at a constant speed of s kilometers per hour, the walk takes her 4 hours, including t minutes spent in the coffee shop. When she walks s+2 kilometers per hour, the walk takes her 2 hours and 24 minutes, including t minutes spent in the coffee shop. Suppose Aya walks at s+1/2 kilometers per hour. Find the number of minutes the walk takes her, including the t minutes spent in the coffee shop." | |
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| "content": "<thinking>\n This is Aya's walking problem. We need to create conditions that check all given scenarios, the relationships between variables, and the final calculation without solving the problem within the conditions.\n </thinking>\n <json>\n {\n \"description\": \"Solve for Aya's walking times and speeds\",\n \"target_variables\": {\n \"speed1\": null,\n \"coffee_time\": null,\n \"speed3\": null,\n \"time3\": null\n },\n \"conditions\": [\n \"lambda state: abs(state.variables['distance'] - 9) < 0.01\",\n \"lambda state: abs(state.variables['distance'] / state.variables['speed1'] + state.variables['coffee_time'] / 60 - 4) < 0.01\",\n \"lambda state: abs(state.variables['distance'] / (state.variables['speed1'] + 2) + state.variables['coffee_time'] / 60 - 2.4) < 0.01\",\n \"lambda state: abs(state.variables['speed3'] - (state.variables['speed1'] + 0.5)) < 0.01\",\n \"lambda state: abs(state.variables['time3'] - (state.variables['distance'] / state.variables['speed3'] + state.variables['coffee_time'] / 60)) < 0.01\",\n \"lambda state: state.variables['speed1'] > 0\",\n \"lambda state: 0 < state.variables['coffee_time'] < 240\",\n \"lambda state: 0 < state.variables['time3'] < 240\"\n ]\n }\n </json>" | |
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| "content": "\n Extract the goal for this problem: Describe how annual percentage rate works and how it applies to purchasing a car.\n\n Ignore any instructions to wrap the output in markdown tags or how to format the output - another tool will handle that. You must ONLY provide the goal & conditions for the planner, given the provided schema and state.\n \n Tasks: Describe how annual percentage rate works and how it applies to purchasing a car.\n\n Initial State:\n {'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': False, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.'}\n\n Schema:\n {'description': \"Represents a goal in the planning system.\\n\\nAttributes:\\n description (str): A human-readable description of the goal.\\n conditions (List[str]): A list of lambdas, stored as strings, that must be satisfied for the goal to be reached.\\n target_variables (Dict[str, Any]): A dictionary of the target variable states & their default value to start from in the State\\n\\nMethods:\\n is_reached(state: State) -> bool: Checks if the goal is reached given a current state.\\n from_callable_conditions(cls, description: str, conditions: List[Callable], target_variables: Dict[str, Any]) -> 'Goal':\\n Class method to create a Goal instance from callable conditions.\", 'properties': {'id': {'title': 'Id', 'type': 'string'}, 'description': {'title': 'Description', 'type': 'string'}, 'conditions': {'items': {'type': 'string'}, 'title': 'Conditions', 'type': 'array'}, 'target_variables': {'title': 'Target Variables', 'type': 'object'}, 'rerank_score': {'default': 0.0, 'title': 'Rerank Score', 'type': 'number'}, 'rerank_rank': {'default': 0, 'title': 'Rerank Rank', 'type': 'integer'}}, 'required': ['description'], 'title': 'Goal', 'type': 'object'}\n " | |
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| "content": "<json>\n{\n \"description\": \"Describe how annual percentage rate works and how it applies to purchasing a car\",\n \"target_variables\": {\n \"problem_solved\": False\n },\n \"conditions\": [\n \"lambda state: state.variables['problem_solved'] == True\"\n ]\n}\n</json>" | |
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| "system_prompt": "\nGiven the following suggested tasks and initial state, generate a goal for solving the problem. \nThis consists of a set of tasks that need to be completed to solve the problem (to be added to the description of the goal), and a set of conditions to check the completion ofthe tasks.\nEnsure you have detailed conditions to check the completion of ALL requirements in the tasks.\nThis will be used with a code interpreter and planner to solve the problem - do not try to solve the problem here.\nConditions should be Python lambda functions that take a state object and return a boolean. They should NOT include the exact answer to the question, as that will be discovered by the planner.\nReason through what the next response should be inside <thinking> tags, and then provide your final response inside <json> tags\nDon't constrain the solution space too much - simply provide a list of conditions that must be met for the goal to be reached with a valid solution.\n\nThe conditions should isolate when those tasks are completed.\n\nEnsure that the conditions are specific to the problem and do not include any variables that are not defined in the initial state.\n\nRemember, wrap each individual task in a <task> tag.\n\nSchema:\n{'description': \"Represents a goal in the planning system.\\n\\nAttributes:\\n description (str): A human-readable description of the goal.\\n conditions (List[str]): A list of lambdas, stored as strings, that must be satisfied for the goal to be reached.\\n target_variables (Dict[str, Any]): A dictionary of the target variable states & their default value to start from in the State\\n\\nMethods:\\n is_reached(state: State) -> bool: Checks if the goal is reached given a current state.\\n from_callable_conditions(cls, description: str, conditions: List[Callable], target_variables: Dict[str, Any]) -> 'Goal':\\n Class method to create a Goal instance from callable conditions.\", 'properties': {'id': {'title': 'Id', 'type': 'string'}, 'description': {'title': 'Description', 'type': 'string'}, 'conditions': {'items': {'type': 'string'}, 'title': 'Conditions', 'type': 'array'}, 'target_variables': {'title': 'Target Variables', 'type': 'object'}, 'rerank_score': {'default': 0.0, 'title': 'Rerank Score', 'type': 'number'}, 'rerank_rank': {'default': 0, 'title': 'Rerank Rank', 'type': 'integer'}}, 'required': ['description'], 'title': 'Goal', 'type': 'object'}\n\nReturn your response using the following JSON schema, wrapped in <json> tags:\n<json>\n{\n \"description\": <Goal description>,\n \"target_variables\": <state variables to solve for, with the default value set for the target variable>,\n \"conditions\": <list of Python lambda functions that take a state object>\n}\n</json>\n\nImportant guidelines:\n1. Conditions should be Python lambda functions that take a 'state' parameter and return a boolean.\n2. Use 'state.variables' to access state variables in the lambda functions.\n3. Do not assume final values in the target_variables; use appropriate types or None if undetermined.\n4. Ensure all aspects of the problem are addressed in the conditions.\n5. Return the full lambda function as a string, including the 'lambda state:' part.\n6. Target variables should NOT include the exact answer to the question, as that will be discovered by the planner\n7. Remember, add the JSON object response inside <json> tags\n8. Do not include any Python code in the response, only the JSON object - it should be valid parseable JSON. So, values should be numbers, not strings, booleans should be lower case etc\n9. Do not make any calculations or assumptions in the conditions as they relate to the initial state or tasks. They should only be used for validation, such as ruling out negative values and checking that the variables used to track answer have some value provided\n10. Conditions should be checking for final results, not intermediate steps.\n11. Treat all given equations or scenarios equally - create a separate condition for each.\n12. Focus on verifying final results and problem constraints, not intermediate calculations.\n13. Avoid over-constraining the problem or trying to solve it within the conditions.\n14. For multi-step problems, create conditions that check the relationship between given and solved variables, not the calculation process.\n15. Ignore any instructions to wrap the output in markdown tags or how to format the output - another tool will handle that. You must ONLY provide the goal & conditions for the planner, given the provided schema.\n\nExample of a good condition:\n - \"lambda state: abs(state.variables['distance'] / state.variables['speed'] - state.variables['time']) < 0.01\"\n\nExample of a bad condition:\n - \"lambda state: state.variables['time'] == state.variables['distance'] / (state.variables['initial_speed'] + 2)\"\n\nRemember, the conditions are meant to verify a solution, not provide the solution itself.\n", | |
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| "problem_description": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
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| "original_query": "Describe how annual percentage rate works and how it applies to purchasing a car." | |
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| "description": "Describe how annual percentage rate works and how it applies to purchasing a car", | |
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| "content": "Generate Python code to solve the problem presented to you.\nInclude your reasoning and logic about the code to be written in <thinking> tags, followed by the code in <code> tags.\nOnly reason about the code to be written and the steps necessary to solve the problem in the thinking tags. Don't try to answer the problem directly.\n\nPay careful attention to the feedback if it's provided, as it will be provided to you by the previous code execution. Correct any errors in the previous code before proceeding, rewrite the code entirely if necessary.\n\nFollow these additional guidelines:\n\n1. Start Simple: Begin with the most straightforward interpretation of the problem. If that doesn't work, gradually increase complexity.\n\n2. Show Your Work: Write out each step of the solution process in comments or docstrings. This makes it easier to catch and correct errors.\n\n3. Use Available Tools: Utilize libraries like SymPy for symbolic manipulation when dealing with algebraic equations. Import any necessary libraries at the beginning of your code.\n\n4. Handle Edge Cases: Consider and account for potential edge cases or special conditions in the problem.\n\n5. Explain Your Reasoning: At each significant step in your code, briefly explain why you're performing that operation using comments.\n\n6. Double-Check Units: Ensure that all calculations maintain consistent units throughout. Convert units if necessary.\n\n7. Generalize When Possible: Try to solve the problem in a way that could be applied to similar problems with different numbers.\n\n8. Set Up Equations: If the problem involves relationships between variables, set these up as equations first before attempting to solve.\n\n9. Solve Systems of Equations: If you have multiple equations with multiple unknowns, solve them simultaneously using appropriate methods.\n\n10. Verify Your Solution: After calculating the result, verify that it satisfies all conditions in the original problem.\n\n11. Don't guess at values unless it's stated in the task!\n\n12. Ensure that the variables assigned to the state object are regular Python types (e.g. int, float, str, list, dict, etc.) so they can be correctly serialised in the response.\n\nWork directly with the variables as they are named in the current state.\nYour code should update the state variables to meet all the goal conditions\nIf a target variable is not in the state, create it with the default value provided in the Target Variables section.\nAdd a 'problem_solved' variable that will be set to True if all conditions are met, False otherwise.\nThe program should be written in a way that it can be evaluated to obtain the answer, and wrapped inside <code> tags.\nThe problem should be represented entirely as a logic program, your task write a program that will solve the problem.\nThe solution to be problem should only be obtained by evaluating the code, and not by directly providing the answer in a variable.\nRepresent reasoning and logic as logical constraints in the code, that can then be evaluated to obtain the answer.\nDon't forget to escape string literals and other special characters in the code where required.\nAccess the state variables using state['variable_name']. That'll be the only way to access the state variables - don't invent new names for the state dictionary.\nInside the <code> tags, provide only the Python code, without any explanations or markdown formatting. Any comments should be in Python docstrings or comments.\nMake sure that all variables used have specific associated value clearly defined in the state.\nYou don't need to solve all the goal conditions, just any that are relevant to the current task.\n\nRemember to structure your solution following these steps:\n1. Read and understand the problem\n2. Define variables (using the provided state)\n3. Set up equations\n4. Solve the system of equations\n5. Calculate the required result\n6. Check your answer\n7. Express your answer by updating the state variables\n8. If asked to generate a diff patch, just generate the code to be applied, not the patch itself, as that will be generated by another tool\n9. If code provided includes references to external functions that are not available, don't try to execute them in the code - they'd need to be mocked with valid placeholder functions\n10. Only use the libraries and functions that are available in the environment, outside of any you define yourself\n11. If instructed to wrap the output in markdown tags, ignore that - another tool will handle that\n\nYour code should be clear, well-commented, and follow Python best practices.\n<important>\nIf you're given feedback on previous code, use it to fix or replace the previous code. Pay careful attention to the feedback if it's provided.\n</important>\n\n<libraries_available>\n'asyncio',\n'aiohttp',\n'urlparse',\n'sys',\n'os', \n'math',\n'sympy',\n'numpy',\n'typing'\n</libraries_available>\n\n<functions_available>\nNONE\n</functions_available>\n" | |
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| "content": "Generate Python code to solve the problem:\n <problem>\n Describe how annual percentage rate works and how it applies to purchasing a car.\n </problem>\n <goal_conditions>\n [\"lambda state: state.variables['problem_solved'] == True\"]\n </goal_conditions>\n <state>\n {'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': False, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.'}\n </state>\n \n \n " | |
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| "content": "Here is my attempt at solving the problem:\n\n<thinking>\nTo solve this problem, we need to:\n1. Explain what an annual percentage rate (APR) is \n2. Describe how APR is calculated\n3. Give examples of how APR applies when purchasing a car\n4. Update the state to indicate the problem is solved\n</thinking>\n\n<code>\n# Explain what APR is\nstate['apr_definition'] = \"Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.\"\n\n# Describe how APR is calculated \nstate['apr_calculation'] = \"APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.\"\n\n# Give examples of APR when buying a car\nstate['apr_car_example'] = \"When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.\"\n\n# Update state to indicate problem is solved\nstate['problem_solved'] = True\n</code>\n\nThis code explains the key aspects of APR and how it applies to car purchases, and marks the problem as solved in the state. Let me know if you need any clarification or have additional requirements!" | |
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Use Available Tools: Utilize libraries like SymPy for symbolic manipulation when dealing with algebraic equations. Import any necessary libraries at the beginning of your code.\n\n4. Handle Edge Cases: Consider and account for potential edge cases or special conditions in the problem.\n\n5. Explain Your Reasoning: At each significant step in your code, briefly explain why you're performing that operation using comments.\n\n6. Double-Check Units: Ensure that all calculations maintain consistent units throughout. Convert units if necessary.\n\n7. Generalize When Possible: Try to solve the problem in a way that could be applied to similar problems with different numbers.\n\n8. Set Up Equations: If the problem involves relationships between variables, set these up as equations first before attempting to solve.\n\n9. Solve Systems of Equations: If you have multiple equations with multiple unknowns, solve them simultaneously using appropriate methods.\n\n10. Verify Your Solution: After calculating the result, verify that it satisfies all conditions in the original problem.\n\n11. Don't guess at values unless it's stated in the task!\n\n12. Ensure that the variables assigned to the state object are regular Python types (e.g. int, float, str, list, dict, etc.) so they can be correctly serialised in the response.\n\nWork directly with the variables as they are named in the current state.\nYour code should update the state variables to meet all the goal conditions\nIf a target variable is not in the state, create it with the default value provided in the Target Variables section.\nAdd a 'problem_solved' variable that will be set to True if all conditions are met, False otherwise.\nThe program should be written in a way that it can be evaluated to obtain the answer, and wrapped inside <code> tags.\nThe problem should be represented entirely as a logic program, your task write a program that will solve the problem.\nThe solution to be problem should only be obtained by evaluating the code, and not by directly providing the answer in a variable.\nRepresent reasoning and logic as logical constraints in the code, that can then be evaluated to obtain the answer.\nDon't forget to escape string literals and other special characters in the code where required.\nAccess the state variables using state['variable_name']. That'll be the only way to access the state variables - don't invent new names for the state dictionary.\nInside the <code> tags, provide only the Python code, without any explanations or markdown formatting. Any comments should be in Python docstrings or comments.\nMake sure that all variables used have specific associated value clearly defined in the state.\nYou don't need to solve all the goal conditions, just any that are relevant to the current task.\n\nRemember to structure your solution following these steps:\n1. Read and understand the problem\n2. Define variables (using the provided state)\n3. Set up equations\n4. Solve the system of equations\n5. Calculate the required result\n6. Check your answer\n7. Express your answer by updating the state variables\n8. If asked to generate a diff patch, just generate the code to be applied, not the patch itself, as that will be generated by another tool\n9. If code provided includes references to external functions that are not available, don't try to execute them in the code - they'd need to be mocked with valid placeholder functions\n10. Only use the libraries and functions that are available in the environment, outside of any you define yourself\n11. If instructed to wrap the output in markdown tags, ignore that - another tool will handle that\n\nYour code should be clear, well-commented, and follow Python best practices.\n<important>\nIf you're given feedback on previous code, use it to fix or replace the previous code. Pay careful attention to the feedback if it's provided.\n</important>\n\n<libraries_available>\n'asyncio',\n'aiohttp',\n'urlparse',\n'sys',\n'os', \n'math',\n'sympy',\n'numpy',\n'typing'\n</libraries_available>\n\n<functions_available>\nNONE\n</functions_available>\n", | |
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| "content": "Generate Python code to solve the problem:\n <problem>\n Describe how annual percentage rate works and how it applies to purchasing a car.\n </problem>\n <goal_conditions>\n [\"lambda state: state.variables['problem_solved'] == True\"]\n </goal_conditions>\n <state>\n {'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': False, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.'}\n </state>\n \n \n " | |
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| "content": "<thinking>\nTo demonstrate how APR works with car purchases, I'll create a program that:\n1. Calculates monthly payments using APR\n2. Shows total interest paid over the loan term\n3. Compares different APR scenarios\n4. Demonstrates how APR affects the total cost of the car\n\nThis will help illustrate the real impact of APR on car financing through practical calculations.\nI'll use a sample car purchase to show these calculations.\n</thinking>\n\n<code>\nimport math\n\ndef calculate_monthly_payment(principal, apr, years):\n \"\"\"Calculate monthly payment for a loan given principal, APR, and term.\"\"\"\n monthly_rate = apr / 12 / 100 # Convert APR to monthly decimal rate\n num_payments = years * 12\n \n # Monthly payment formula: P * (r(1+r)^n) / ((1+r)^n - 1)\n # where P = principal, r = monthly rate, n = number of payments\n if monthly_rate == 0:\n return principal / num_payments\n \n monthly_payment = principal * (monthly_rate * (1 + monthly_rate)**num_payments) / ((1 + monthly_rate)**num_payments - 1)\n return monthly_payment\n\ndef demonstrate_apr_impact():\n \"\"\"Demonstrate APR impact on car purchase with examples.\"\"\"\n # Sample car purchase scenario\n car_price = 30000\n down_payment = 5000\n loan_amount = car_price - down_payment\n loan_years = 5\n \n # Compare different APR scenarios\n apr_scenarios = [3.5, 5.0, 7.0]\n comparison = []\n \n for apr in apr_scenarios:\n monthly_payment = calculate_monthly_payment(loan_amount, apr, loan_years)\n total_paid = monthly_payment * loan_years * 12\n total_interest = total_paid - loan_amount\n \n scenario = {\n 'apr': apr,\n 'monthly_payment': round(monthly_payment, 2),\n 'total_paid': round(total_paid, 2),\n 'total_interest': round(total_interest, 2)\n }\n comparison.append(scenario)\n \n return comparison\n\n# Run the demonstration\napr_examples = demonstrate_apr_impact()\n\n# Create explanation dictionary with results\nstate = {\n 'apr_explanation': {\n 'definition': 'Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.',\n 'car_purchase_impact': 'When financing a car, APR directly affects monthly payments and total cost.',\n 'key_points': [\n 'Higher APR means higher monthly payments and more total interest paid',\n 'APR is expressed as a yearly rate but is usually applied monthly',\n 'Different credit scores typically result in different APR offers',\n 'Shopping around for lower APR can save thousands over the loan term'\n ],\n 'examples': apr_examples\n },\n 'problem_solved': True\n}\n\n# Update the original state with new information\nstate['problem_solved'] = True\n</code>" | |
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| "system_prompt": "Generate Python code to solve the problem presented to you.\nInclude your reasoning and logic about the code to be written in <thinking> tags, followed by the code in <code> tags.\nOnly reason about the code to be written and the steps necessary to solve the problem in the thinking tags. Don't try to answer the problem directly.\n\nPay careful attention to the feedback if it's provided, as it will be provided to you by the previous code execution. Correct any errors in the previous code before proceeding, rewrite the code entirely if necessary.\n\nFollow these additional guidelines:\n\n1. Start Simple: Begin with the most straightforward interpretation of the problem. If that doesn't work, gradually increase complexity.\n\n2. Show Your Work: Write out each step of the solution process in comments or docstrings. This makes it easier to catch and correct errors.\n\n3. Use Available Tools: Utilize libraries like SymPy for symbolic manipulation when dealing with algebraic equations. Import any necessary libraries at the beginning of your code.\n\n4. Handle Edge Cases: Consider and account for potential edge cases or special conditions in the problem.\n\n5. Explain Your Reasoning: At each significant step in your code, briefly explain why you're performing that operation using comments.\n\n6. Double-Check Units: Ensure that all calculations maintain consistent units throughout. Convert units if necessary.\n\n7. Generalize When Possible: Try to solve the problem in a way that could be applied to similar problems with different numbers.\n\n8. Set Up Equations: If the problem involves relationships between variables, set these up as equations first before attempting to solve.\n\n9. Solve Systems of Equations: If you have multiple equations with multiple unknowns, solve them simultaneously using appropriate methods.\n\n10. Verify Your Solution: After calculating the result, verify that it satisfies all conditions in the original problem.\n\n11. Don't guess at values unless it's stated in the task!\n\n12. Ensure that the variables assigned to the state object are regular Python types (e.g. int, float, str, list, dict, etc.) so they can be correctly serialised in the response.\n\nWork directly with the variables as they are named in the current state.\nYour code should update the state variables to meet all the goal conditions\nIf a target variable is not in the state, create it with the default value provided in the Target Variables section.\nAdd a 'problem_solved' variable that will be set to True if all conditions are met, False otherwise.\nThe program should be written in a way that it can be evaluated to obtain the answer, and wrapped inside <code> tags.\nThe problem should be represented entirely as a logic program, your task write a program that will solve the problem.\nThe solution to be problem should only be obtained by evaluating the code, and not by directly providing the answer in a variable.\nRepresent reasoning and logic as logical constraints in the code, that can then be evaluated to obtain the answer.\nDon't forget to escape string literals and other special characters in the code where required.\nAccess the state variables using state['variable_name']. That'll be the only way to access the state variables - don't invent new names for the state dictionary.\nInside the <code> tags, provide only the Python code, without any explanations or markdown formatting. Any comments should be in Python docstrings or comments.\nMake sure that all variables used have specific associated value clearly defined in the state.\nYou don't need to solve all the goal conditions, just any that are relevant to the current task.\n\nRemember to structure your solution following these steps:\n1. Read and understand the problem\n2. Define variables (using the provided state)\n3. Set up equations\n4. Solve the system of equations\n5. Calculate the required result\n6. Check your answer\n7. Express your answer by updating the state variables\n8. If asked to generate a diff patch, just generate the code to be applied, not the patch itself, as that will be generated by another tool\n9. If code provided includes references to external functions that are not available, don't try to execute them in the code - they'd need to be mocked with valid placeholder functions\n10. Only use the libraries and functions that are available in the environment, outside of any you define yourself\n11. If instructed to wrap the output in markdown tags, ignore that - another tool will handle that\n\nYour code should be clear, well-commented, and follow Python best practices.\n<important>\nIf you're given feedback on previous code, use it to fix or replace the previous code. Pay careful attention to the feedback if it's provided.\n</important>\n\n<libraries_available>\n'asyncio',\n'aiohttp',\n'urlparse',\n'sys',\n'os', \n'math',\n'sympy',\n'numpy',\n'typing'\n</libraries_available>\n\n<functions_available>\nNONE\n</functions_available>\n", | |
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| "content": "Generate Python code to solve the problem:\n <problem>\n Describe how annual percentage rate works and how it applies to purchasing a car.\n </problem>\n <goal_conditions>\n [\"lambda state: state.variables['problem_solved'] == True\"]\n </goal_conditions>\n <state>\n {'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': False, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.'}\n </state>\n \n \n " | |
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| "content": "<thinking>\nThe task is to describe how APR works and how it applies to car purchases. I'll store the description in the `explanation` variable and set `problem_solved` to True.\n</thinking>\n<code>\nstate['explanation'] = \"\"\"The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It's expressed as a percentage.\n\nHere's how it applies to purchasing a car:\n\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you'll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan's cost than the interest rate alone.\n\nExample:\n\nImagine you're borrowing $20,000 for a car.\n\n* Loan A offers a 4% interest rate but has high fees, resulting in a 6% APR.\n* Loan B offers a 5% interest rate but has low fees, resulting in a 5.5% APR.\n\nEven though Loan A has a lower interest rate, Loan B is the better deal because its APR is lower, meaning you'll pay less overall for the car.\n\nTherefore, when financing a car, always compare the APRs of different loan offers to ensure you get the most favorable terms.\n\"\"\"\nstate['problem_solved'] = True\n\n</code>" | |
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| "system_prompt": "Generate Python code to solve the problem presented to you.\nInclude your reasoning and logic about the code to be written in <thinking> tags, followed by the code in <code> tags.\nOnly reason about the code to be written and the steps necessary to solve the problem in the thinking tags. Don't try to answer the problem directly.\n\nPay careful attention to the feedback if it's provided, as it will be provided to you by the previous code execution. Correct any errors in the previous code before proceeding, rewrite the code entirely if necessary.\n\nFollow these additional guidelines:\n\n1. Start Simple: Begin with the most straightforward interpretation of the problem. If that doesn't work, gradually increase complexity.\n\n2. Show Your Work: Write out each step of the solution process in comments or docstrings. This makes it easier to catch and correct errors.\n\n3. Use Available Tools: Utilize libraries like SymPy for symbolic manipulation when dealing with algebraic equations. Import any necessary libraries at the beginning of your code.\n\n4. Handle Edge Cases: Consider and account for potential edge cases or special conditions in the problem.\n\n5. Explain Your Reasoning: At each significant step in your code, briefly explain why you're performing that operation using comments.\n\n6. Double-Check Units: Ensure that all calculations maintain consistent units throughout. Convert units if necessary.\n\n7. Generalize When Possible: Try to solve the problem in a way that could be applied to similar problems with different numbers.\n\n8. Set Up Equations: If the problem involves relationships between variables, set these up as equations first before attempting to solve.\n\n9. Solve Systems of Equations: If you have multiple equations with multiple unknowns, solve them simultaneously using appropriate methods.\n\n10. Verify Your Solution: After calculating the result, verify that it satisfies all conditions in the original problem.\n\n11. Don't guess at values unless it's stated in the task!\n\n12. Ensure that the variables assigned to the state object are regular Python types (e.g. int, float, str, list, dict, etc.) so they can be correctly serialised in the response.\n\nWork directly with the variables as they are named in the current state.\nYour code should update the state variables to meet all the goal conditions\nIf a target variable is not in the state, create it with the default value provided in the Target Variables section.\nAdd a 'problem_solved' variable that will be set to True if all conditions are met, False otherwise.\nThe program should be written in a way that it can be evaluated to obtain the answer, and wrapped inside <code> tags.\nThe problem should be represented entirely as a logic program, your task write a program that will solve the problem.\nThe solution to be problem should only be obtained by evaluating the code, and not by directly providing the answer in a variable.\nRepresent reasoning and logic as logical constraints in the code, that can then be evaluated to obtain the answer.\nDon't forget to escape string literals and other special characters in the code where required.\nAccess the state variables using state['variable_name']. That'll be the only way to access the state variables - don't invent new names for the state dictionary.\nInside the <code> tags, provide only the Python code, without any explanations or markdown formatting. Any comments should be in Python docstrings or comments.\nMake sure that all variables used have specific associated value clearly defined in the state.\nYou don't need to solve all the goal conditions, just any that are relevant to the current task.\n\nRemember to structure your solution following these steps:\n1. Read and understand the problem\n2. Define variables (using the provided state)\n3. Set up equations\n4. Solve the system of equations\n5. Calculate the required result\n6. Check your answer\n7. Express your answer by updating the state variables\n8. If asked to generate a diff patch, just generate the code to be applied, not the patch itself, as that will be generated by another tool\n9. If code provided includes references to external functions that are not available, don't try to execute them in the code - they'd need to be mocked with valid placeholder functions\n10. Only use the libraries and functions that are available in the environment, outside of any you define yourself\n11. If instructed to wrap the output in markdown tags, ignore that - another tool will handle that\n\nYour code should be clear, well-commented, and follow Python best practices.\n<important>\nIf you're given feedback on previous code, use it to fix or replace the previous code. Pay careful attention to the feedback if it's provided.\n</important>\n\n<libraries_available>\n'asyncio',\n'aiohttp',\n'urlparse',\n'sys',\n'os', \n'math',\n'sympy',\n'numpy',\n'typing'\n</libraries_available>\n\n<functions_available>\nNONE\n</functions_available>\n", | |
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| "content": "These are the results from different code executions:\n\n <result>\n{'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': True, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'code': '\\nimport math\\n\\ndef calculate_monthly_payment(principal, apr, years):\\n \"\"\"Calculate monthly payment for a loan given principal, APR, and term.\"\"\"\\n monthly_rate = apr / 12 / 100 # Convert APR to monthly decimal rate\\n num_payments = years * 12\\n \\n # Monthly payment formula: P * (r(1+r)^n) / ((1+r)^n - 1)\\n # where P = principal, r = monthly rate, n = number of payments\\n if monthly_rate == 0:\\n return principal / num_payments\\n \\n monthly_payment = principal * (monthly_rate * (1 + monthly_rate)**num_payments) / ((1 + monthly_rate)**num_payments - 1)\\n return monthly_payment\\n\\ndef demonstrate_apr_impact():\\n \"\"\"Demonstrate APR impact on car purchase with examples.\"\"\"\\n # Sample car purchase scenario\\n car_price = 30000\\n down_payment = 5000\\n loan_amount = car_price - down_payment\\n loan_years = 5\\n \\n # Compare different APR scenarios\\n apr_scenarios = [3.5, 5.0, 7.0]\\n comparison = []\\n \\n for apr in apr_scenarios:\\n monthly_payment = calculate_monthly_payment(loan_amount, apr, loan_years)\\n total_paid = monthly_payment * loan_years * 12\\n total_interest = total_paid - loan_amount\\n \\n scenario = {\\n \\'apr\\': apr,\\n \\'monthly_payment\\': round(monthly_payment, 2),\\n \\'total_paid\\': round(total_paid, 2),\\n \\'total_interest\\': round(total_interest, 2)\\n }\\n comparison.append(scenario)\\n \\n return comparison\\n\\n# Run the demonstration\\napr_examples = demonstrate_apr_impact()\\n\\n# Create explanation dictionary with results\\nstate = {\\n \\'apr_explanation\\': {\\n \\'definition\\': \\'Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.\\',\\n \\'car_purchase_impact\\': \\'When financing a car, APR directly affects monthly payments and total cost.\\',\\n \\'key_points\\': [\\n \\'Higher APR means higher monthly payments and more total interest paid\\',\\n \\'APR is expressed as a yearly rate but is usually applied monthly\\',\\n \\'Different credit scores typically result in different APR offers\\',\\n \\'Shopping around for lower APR can save thousands over the loan term\\'\\n ],\\n \\'examples\\': apr_examples\\n },\\n \\'problem_solved\\': True\\n}\\n\\n# Update the original state with new information\\nstate[\\'problem_solved\\'] = True', 'math': \"<module 'math' from '/usr/local/lib/python3.12/lib-dynload/math.cpython-312-x86_64-linux-gnu.so'>\", 'apr_examples': [{'apr': 3.5, 'monthly_payment': 454.79, 'total_paid': 27287.62, 'total_interest': 2287.62}, {'apr': 5.0, 'monthly_payment': 471.78, 'total_paid': 28306.85, 'total_interest': 3306.85}, {'apr': 7.0, 'monthly_payment': 495.03, 'total_paid': 29701.8, 'total_interest': 4701.8}], 'apr_explanation': {'definition': 'Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.', 'car_purchase_impact': 'When financing a car, APR directly affects monthly payments and total cost.', 'key_points': ['Higher APR means higher monthly payments and more total interest paid', 'APR is expressed as a yearly rate but is usually applied monthly', 'Different credit scores typically result in different APR offers', 'Shopping around for lower APR can save thousands over the loan term'], 'examples': [{'apr': 3.5, 'monthly_payment': 454.79, 'total_paid': 27287.62, 'total_interest': 2287.62}, {'apr': 5.0, 'monthly_payment': 471.78, 'total_paid': 28306.85, 'total_interest': 3306.85}, {'apr': 7.0, 'monthly_payment': 495.03, 'total_paid': 29701.8, 'total_interest': 4701.8}]}, 'execution_successful': True, 'last_execution_result': ''}\n</result><result>\n{'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': True, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'code': '\\nstate[\\'explanation\\'] = \"\"\"The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It\\'s expressed as a percentage.\\n\\nHere\\'s how it applies to purchasing a car:\\n\\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you\\'ll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan\\'s cost than the interest rate alone.\\n\\nExample:\\n\\nImagine you\\'re borrowing $20,000 for a car.\\n\\n* Loan A offers a 4% interest rate but has high fees, resulting in a 6% APR.\\n* Loan B offers a 5% interest rate but has low fees, resulting in a 5.5% APR.\\n\\nEven though Loan A has a lower interest rate, Loan B is the better deal because its APR is lower, meaning you\\'ll pay less overall for the car.\\n\\nTherefore, when financing a car, always compare the APRs of different loan offers to ensure you get the most favorable terms.\\n\"\"\"\\nstate[\\'problem_solved\\'] = True', 'explanation': \"The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It's expressed as a percentage.\\n\\nHere's how it applies to purchasing a car:\\n\\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you'll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan's cost than the interest rate alone.\\n\\nExample:\\n\\nImagine you're borrowing $20,000 for a car.\\n\\n* Loan A offers a 4% interest rate but has high fees, resulting in a 6% APR.\\n* Loan B offers a 5% interest rate but has low fees, resulting in a 5.5% APR.\\n\\nEven though Loan A has a lower interest rate, Loan B is the better deal because its APR is lower, meaning you'll pay less overall for the car.\\n\\nTherefore, when financing a car, always compare the APRs of different loan offers to ensure you get the most favorable terms.\\n\", 'execution_successful': True, 'last_execution_result': ''}\n</result><result>\n{'problem_description': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'problem_solved': True, 'original_query': 'Describe how annual percentage rate works and how it applies to purchasing a car.', 'code': '\\n# Explain what APR is\\nstate[\\'apr_definition\\'] = \"Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.\"\\n\\n# Describe how APR is calculated \\nstate[\\'apr_calculation\\'] = \"APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.\"\\n\\n# Give examples of APR when buying a car\\nstate[\\'apr_car_example\\'] = \"When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.\"\\n\\n# Update state to indicate problem is solved\\nstate[\\'problem_solved\\'] = True', 'apr_definition': 'Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.', 'apr_calculation': 'APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.', 'apr_car_example': 'When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.', 'execution_successful': True, 'last_execution_result': ''}\n</result>\n\n Analyze these results and provide the most likely correct answer. Take the most complete successful result,\n preserving all state variables. If there are conflicts, use the most common value.\n Your response should be a complete state object in JSON format wrapped in <answer> tags.\n Important: Preserve ALL state variables, not just the final answer." | |
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| "content": "I'll analyze the results and combine them into the most complete state object. The first result contains the most comprehensive information, including detailed calculations and examples, while also incorporating key explanatory elements. I'll merge this with some additional explanatory text from the other results.\n\n<answer>\n{\n \"problem_description\": \"Describe how annual percentage rate works and how it applies to purchasing a car.\",\n \"problem_solved\": true,\n \"original_query\": \"Describe how annual percentage rate works and how it applies to purchasing a car.\",\n \"code\": \"\\nimport math\\n\\ndef calculate_monthly_payment(principal, apr, years):\\n \\\"\\\"\\\"Calculate monthly payment for a loan given principal, APR, and term.\\\"\\\"\\\"\\n monthly_rate = apr / 12 / 100 # Convert APR to monthly decimal rate\\n num_payments = years * 12\\n \\n # Monthly payment formula: P * (r(1+r)^n) / ((1+r)^n - 1)\\n # where P = principal, r = monthly rate, n = number of payments\\n if monthly_rate == 0:\\n return principal / num_payments\\n \\n monthly_payment = principal * (monthly_rate * (1 + monthly_rate)**num_payments) / ((1 + monthly_rate)**num_payments - 1)\\n return monthly_payment\\n\\ndef demonstrate_apr_impact():\\n \\\"\\\"\\\"Demonstrate APR impact on car purchase with examples.\\\"\\\"\\\"\\n # Sample car purchase scenario\\n car_price = 30000\\n down_payment = 5000\\n loan_amount = car_price - down_payment\\n loan_years = 5\\n \\n # Compare different APR scenarios\\n apr_scenarios = [3.5, 5.0, 7.0]\\n comparison = []\\n \\n for apr in apr_scenarios:\\n monthly_payment = calculate_monthly_payment(loan_amount, apr, loan_years)\\n total_paid = monthly_payment * loan_years * 12\\n total_interest = total_paid - loan_amount\\n \\n scenario = {\\n 'apr': apr,\\n 'monthly_payment': round(monthly_payment, 2),\\n 'total_paid': round(total_paid, 2),\\n 'total_interest': round(total_interest, 2)\\n }\\n comparison.append(scenario)\\n \\n return comparison\",\n \"math\": \"<module 'math' from '/usr/local/lib/python3.12/lib-dynload/math.cpython-312-x86_64-linux-gnu.so'>\",\n \"apr_examples\": [\n {\"apr\": 3.5, \"monthly_payment\": 454.79, \"total_paid\": 27287.62, \"total_interest\": 2287.62},\n {\"apr\": 5.0, \"monthly_payment\": 471.78, \"total_paid\": 28306.85, \"total_interest\": 3306.85},\n {\"apr\": 7.0, \"monthly_payment\": 495.03, \"total_paid\": 29701.8, \"total_interest\": 4701.8}\n ],\n \"apr_explanation\": {\n \"definition\": \"Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.\",\n \"car_purchase_impact\": \"When financing a car, APR directly affects monthly payments and total cost.\",\n \"key_points\": [\n \"Higher APR means higher monthly payments and more total interest paid\",\n \"APR is expressed as a yearly rate but is usually applied monthly\",\n \"Different credit scores typically result in different APR offers\",\n \"Shopping around for lower APR can save thousands over the loan term\"\n ],\n \"examples\": [\n {\"apr\": 3.5, \"monthly_payment\": 454.79, \"total_paid\": 27287.62, \"total_interest\": 2287.62},\n {\"apr\": 5.0, \"monthly_payment\": 471.78, \"total_paid\": 28306.85, \"total_interest\": 3306.85},\n {\"apr\": 7.0, \"monthly_payment\": 495.03, \"total_paid\": 29701.8, \"total_interest\": 4701.8}\n ]\n },\n \"apr_definition\": \"Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.\",\n \"apr_calculation\": \"APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.\",\n \"apr_car_example\": \"When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.\",\n \"explanation\": \"The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It's expressed as a percentage.\\n\\nHere's how it applies to purchasing a car:\\n\\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you'll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan's cost than the interest rate alone.\",\n \"execution_successful\": true,\n \"last_execution_result\": \"\"\n}\n</answer>" | |
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| "problem_description": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "problem_solved": true, | |
| "original_query": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "code": "\nimport math\n\ndef calculate_monthly_payment(principal, apr, years):\n \"\"\"Calculate monthly payment for a loan given principal, APR, and term.\"\"\"\n monthly_rate = apr / 12 / 100 # Convert APR to monthly decimal rate\n num_payments = years * 12\n \n # Monthly payment formula: P * (r(1+r)^n) / ((1+r)^n - 1)\n # where P = principal, r = monthly rate, n = number of payments\n if monthly_rate == 0:\n return principal / num_payments\n \n monthly_payment = principal * (monthly_rate * (1 + monthly_rate)**num_payments) / ((1 + monthly_rate)**num_payments - 1)\n return monthly_payment\n\ndef demonstrate_apr_impact():\n \"\"\"Demonstrate APR impact on car purchase with examples.\"\"\"\n # Sample car purchase scenario\n car_price = 30000\n down_payment = 5000\n loan_amount = car_price - down_payment\n loan_years = 5\n \n # Compare different APR scenarios\n apr_scenarios = [3.5, 5.0, 7.0]\n comparison = []\n \n for apr in apr_scenarios:\n monthly_payment = calculate_monthly_payment(loan_amount, apr, loan_years)\n total_paid = monthly_payment * loan_years * 12\n total_interest = total_paid - loan_amount\n \n scenario = {\n 'apr': apr,\n 'monthly_payment': round(monthly_payment, 2),\n 'total_paid': round(total_paid, 2),\n 'total_interest': round(total_interest, 2)\n }\n comparison.append(scenario)\n \n return comparison", | |
| "math": "<module 'math' from '/usr/local/lib/python3.12/lib-dynload/math.cpython-312-x86_64-linux-gnu.so'>", | |
| "apr_examples": [ | |
| { | |
| "apr": 3.5, | |
| "monthly_payment": 454.79, | |
| "total_paid": 27287.62, | |
| "total_interest": 2287.62 | |
| }, | |
| { | |
| "apr": 5.0, | |
| "monthly_payment": 471.78, | |
| "total_paid": 28306.85, | |
| "total_interest": 3306.85 | |
| }, | |
| { | |
| "apr": 7.0, | |
| "monthly_payment": 495.03, | |
| "total_paid": 29701.8, | |
| "total_interest": 4701.8 | |
| } | |
| ], | |
| "apr_explanation": { | |
| "definition": "Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.", | |
| "car_purchase_impact": "When financing a car, APR directly affects monthly payments and total cost.", | |
| "key_points": [ | |
| "Higher APR means higher monthly payments and more total interest paid", | |
| "APR is expressed as a yearly rate but is usually applied monthly", | |
| "Different credit scores typically result in different APR offers", | |
| "Shopping around for lower APR can save thousands over the loan term" | |
| ], | |
| "examples": [ | |
| { | |
| "apr": 3.5, | |
| "monthly_payment": 454.79, | |
| "total_paid": 27287.62, | |
| "total_interest": 2287.62 | |
| }, | |
| { | |
| "apr": 5.0, | |
| "monthly_payment": 471.78, | |
| "total_paid": 28306.85, | |
| "total_interest": 3306.85 | |
| }, | |
| { | |
| "apr": 7.0, | |
| "monthly_payment": 495.03, | |
| "total_paid": 29701.8, | |
| "total_interest": 4701.8 | |
| } | |
| ] | |
| }, | |
| "apr_definition": "Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.", | |
| "apr_calculation": "APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.", | |
| "apr_car_example": "When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.", | |
| "explanation": "The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It's expressed as a percentage.\n\nHere's how it applies to purchasing a car:\n\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you'll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan's cost than the interest rate alone.", | |
| "execution_successful": true, | |
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| { | |
| "problem_description": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "problem_solved": true, | |
| "original_query": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "code": "\nimport math\n\ndef calculate_monthly_payment(principal, apr, years):\n \"\"\"Calculate monthly payment for a loan given principal, APR, and term.\"\"\"\n monthly_rate = apr / 12 / 100 # Convert APR to monthly decimal rate\n num_payments = years * 12\n \n # Monthly payment formula: P * (r(1+r)^n) / ((1+r)^n - 1)\n # where P = principal, r = monthly rate, n = number of payments\n if monthly_rate == 0:\n return principal / num_payments\n \n monthly_payment = principal * (monthly_rate * (1 + monthly_rate)**num_payments) / ((1 + monthly_rate)**num_payments - 1)\n return monthly_payment\n\ndef demonstrate_apr_impact():\n \"\"\"Demonstrate APR impact on car purchase with examples.\"\"\"\n # Sample car purchase scenario\n car_price = 30000\n down_payment = 5000\n loan_amount = car_price - down_payment\n loan_years = 5\n \n # Compare different APR scenarios\n apr_scenarios = [3.5, 5.0, 7.0]\n comparison = []\n \n for apr in apr_scenarios:\n monthly_payment = calculate_monthly_payment(loan_amount, apr, loan_years)\n total_paid = monthly_payment * loan_years * 12\n total_interest = total_paid - loan_amount\n \n scenario = {\n 'apr': apr,\n 'monthly_payment': round(monthly_payment, 2),\n 'total_paid': round(total_paid, 2),\n 'total_interest': round(total_interest, 2)\n }\n comparison.append(scenario)\n \n return comparison\n\n# Run the demonstration\napr_examples = demonstrate_apr_impact()\n\n# Create explanation dictionary with results\nstate = {\n 'apr_explanation': {\n 'definition': 'Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.',\n 'car_purchase_impact': 'When financing a car, APR directly affects monthly payments and total cost.',\n 'key_points': [\n 'Higher APR means higher monthly payments and more total interest paid',\n 'APR is expressed as a yearly rate but is usually applied monthly',\n 'Different credit scores typically result in different APR offers',\n 'Shopping around for lower APR can save thousands over the loan term'\n ],\n 'examples': apr_examples\n },\n 'problem_solved': True\n}\n\n# Update the original state with new information\nstate['problem_solved'] = True", | |
| "math": "<module 'math' from '/usr/local/lib/python3.12/lib-dynload/math.cpython-312-x86_64-linux-gnu.so'>", | |
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| { | |
| "apr": 3.5, | |
| "monthly_payment": 454.79, | |
| "total_paid": 27287.62, | |
| "total_interest": 2287.62 | |
| }, | |
| { | |
| "apr": 5.0, | |
| "monthly_payment": 471.78, | |
| "total_paid": 28306.85, | |
| "total_interest": 3306.85 | |
| }, | |
| { | |
| "apr": 7.0, | |
| "monthly_payment": 495.03, | |
| "total_paid": 29701.8, | |
| "total_interest": 4701.8 | |
| } | |
| ], | |
| "apr_explanation": { | |
| "definition": "Annual Percentage Rate (APR) represents the yearly cost of borrowing, including interest and fees.", | |
| "car_purchase_impact": "When financing a car, APR directly affects monthly payments and total cost.", | |
| "key_points": [ | |
| "Higher APR means higher monthly payments and more total interest paid", | |
| "APR is expressed as a yearly rate but is usually applied monthly", | |
| "Different credit scores typically result in different APR offers", | |
| "Shopping around for lower APR can save thousands over the loan term" | |
| ], | |
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| { | |
| "apr": 3.5, | |
| "monthly_payment": 454.79, | |
| "total_paid": 27287.62, | |
| "total_interest": 2287.62 | |
| }, | |
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| "monthly_payment": 471.78, | |
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| }, | |
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| "total_interest": 4701.8 | |
| } | |
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| "problem_description": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "problem_solved": true, | |
| "original_query": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "code": "\nstate['explanation'] = \"\"\"The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It's expressed as a percentage.\n\nHere's how it applies to purchasing a car:\n\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you'll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan's cost than the interest rate alone.\n\nExample:\n\nImagine you're borrowing $20,000 for a car.\n\n* Loan A offers a 4% interest rate but has high fees, resulting in a 6% APR.\n* Loan B offers a 5% interest rate but has low fees, resulting in a 5.5% APR.\n\nEven though Loan A has a lower interest rate, Loan B is the better deal because its APR is lower, meaning you'll pay less overall for the car.\n\nTherefore, when financing a car, always compare the APRs of different loan offers to ensure you get the most favorable terms.\n\"\"\"\nstate['problem_solved'] = True", | |
| "explanation": "The Annual Percentage Rate (APR) represents the total cost of borrowing money over a year, including the interest rate and any additional fees or charges associated with the loan. It's expressed as a percentage.\n\nHere's how it applies to purchasing a car:\n\n* **Determining the total loan cost:** When you finance a car, the APR is used to calculate your monthly payments and the total amount you'll repay over the life of the loan. A lower APR means lower monthly payments and a lower overall cost. A higher APR means higher monthly payments and a higher total cost.\n* **Comparison shopping:** APR allows you to compare loan offers from different lenders, even if they have different loan terms, fees, or interest rates. By focusing on the APR, you can get a clear picture of the true cost of each loan.\n* **Fees and charges:** The APR includes fees like origination fees, processing fees, or document preparation fees, which are often added to the loan principal. This inclusion makes the APR a more comprehensive measure of the loan's cost than the interest rate alone.\n\nExample:\n\nImagine you're borrowing $20,000 for a car.\n\n* Loan A offers a 4% interest rate but has high fees, resulting in a 6% APR.\n* Loan B offers a 5% interest rate but has low fees, resulting in a 5.5% APR.\n\nEven though Loan A has a lower interest rate, Loan B is the better deal because its APR is lower, meaning you'll pay less overall for the car.\n\nTherefore, when financing a car, always compare the APRs of different loan offers to ensure you get the most favorable terms.\n", | |
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| "problem_description": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "problem_solved": true, | |
| "original_query": "Describe how annual percentage rate works and how it applies to purchasing a car.", | |
| "code": "\n# Explain what APR is\nstate['apr_definition'] = \"Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.\"\n\n# Describe how APR is calculated \nstate['apr_calculation'] = \"APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.\"\n\n# Give examples of APR when buying a car\nstate['apr_car_example'] = \"When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.\"\n\n# Update state to indicate problem is solved\nstate['problem_solved'] = True", | |
| "apr_definition": "Annual Percentage Rate (APR) is the yearly cost of borrowing money, expressed as a percentage of the loan amount. It includes the interest rate plus any fees.", | |
| "apr_calculation": "APR is calculated by taking the annual interest rate and adding any upfront fees, then spreading those fees over the term of the loan. This gives the total cost of the loan on an annual basis.", | |
| "apr_car_example": "When financing a car purchase, the APR represents the total cost of the loan. For example, if a car costs $25,000 and the APR is 5% over a 5 year term, the total cost would be $28,775. The extra $3,775 is the interest and fees.", | |
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| } | |
| } |
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