mirror of
https://github.com/InternLM/InternBootcamp.git
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64 lines
35 KiB
JSON
Executable file
64 lines
35 KiB
JSON
Executable file
{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "2 x + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "2 e^{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x^{3}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{3}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\frac{1}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": -2.0, "x_value": 3.1416}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": -1.0, "x_value": 3.1416}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + e^{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 6.2832, "x_value": 3.1416}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 4.7124.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 9.637, "x_value": 4.7124}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = x^{3}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "x^{3}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 0.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 4.1933, "x_value": 0.7854}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 0.7854.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 3.4665, "x_value": 0.7854}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x^{3}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x^{3}", "problem_type": "evaluate", "correct_answer": 35.8922, "x_value": 3.1416}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x^{3}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x^{3}", "problem_type": "expression", "correct_answer": "3 x^{2} + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x^{2}\n\nFind the numerical value of f□g at x = 4.7124.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x^{2}", "problem_type": "evaluate", "correct_answer": 18.8496, "x_value": 4.7124}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "\\frac{1}{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 9.7744, "x_value": 2}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "e^{x}", "problem_type": "expression", "correct_answer": "e^{x} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 4.7124.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 111.319, "x_value": 4.7124}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + e^{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x^{3}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{3}", "problem_type": "evaluate", "correct_answer": 12.5, "x_value": 2}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "x", "problem_type": "expression", "correct_answer": "2", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\frac{2}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\cos{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\cos{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} - \\sin{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "- \\sin{\\left(x \\right)} + \\cos{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\tan{\\left(x \\right)}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\tan{\\left(x \\right)}", "g": "x", "problem_type": "expression", "correct_answer": "\\tan^{2}{\\left(x \\right)} + 2", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = \\log{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 1.5708.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\log{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": -0.3634, "x_value": 1.5708}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "2 x + \\frac{1}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 1.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = \\sqrt{x}\n\nFind the numerical value of f□g at x = 1.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "\\sqrt{x}", "problem_type": "evaluate", "correct_answer": -0.3415, "x_value": 1}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = x\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "x", "problem_type": "evaluate", "correct_answer": 0.0, "x_value": 3.1416}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\cos{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\cos{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 0.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "e^{x} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sqrt{x}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "problem_type": "evaluate", "correct_answer": 7.7426, "x_value": 2}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = \\log{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "\\log{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "2 x + \\frac{1}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{2}\ng(x) = x^{2}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{2}", "g": "x^{2}", "problem_type": "expression", "correct_answer": "4 x", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\tan{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\tan{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\tan^{2}{\\left(x \\right)} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 17.7744, "x_value": 2}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = e^{x}\n\nFind the numerical value of f□g at x = 0.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "e^{x}", "problem_type": "evaluate", "correct_answer": 2.0, "x_value": 0}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sin{\\left(x \\right)}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sin{\\left(x \\right)}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "\\cos{\\left(x \\right)} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "x", "problem_type": "expression", "correct_answer": "3 x^{2} + 1", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\log{\\left(x \\right)}\ng(x) = x\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\log{\\left(x \\right)}", "g": "x", "problem_type": "expression", "correct_answer": "1 + \\frac{1}{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\tan{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.1416.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\tan{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 1.2821, "x_value": 3.1416}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = e^{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "e^{x}", "problem_type": "expression", "correct_answer": "3 x^{2} + e^{x}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = e^{x}\ng(x) = \\sqrt{x}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "e^{x}", "g": "\\sqrt{x}", "problem_type": "expression", "correct_answer": "e^{x} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\sqrt{x}\ng(x) = \\cos{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\sqrt{x}", "g": "\\cos{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "- \\sin{\\left(x \\right)} + \\frac{1}{2 \\sqrt{x}}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x^{3}\ng(x) = x^{3}\n\nFind the numerical value of f□g at x = 3.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x^{3}", "g": "x^{3}", "problem_type": "evaluate", "correct_answer": 54.0, "x_value": 3}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\sin{\\left(x \\right)}\n\nFind the numerical value of f□g at x = 3.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\sin{\\left(x \\right)}", "problem_type": "evaluate", "correct_answer": 0.01, "x_value": 3}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = x\ng(x) = \\cos{\\left(x \\right)}\n\nCompute the expression for f□g.\nPresent your answer in LaTeX within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "x", "g": "\\cos{\\left(x \\right)}", "problem_type": "expression", "correct_answer": "1 - \\sin{\\left(x \\right)}", "x_value": null}}
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{"data_source": "KorOperationUnicode25a1", "prompt": "You are a calculus expert. Solve the problem using the following rules:\nThe operation f□g is defined as f'(x) + g'(x), where f' and g' are derivatives with respect to x.\n\nGiven:\nf(x) = \\cos{\\left(x \\right)}\ng(x) = x^{3}\n\nFind the numerical value of f□g at x = 2.\nProvide a single number within [[ ]].\nExample: [[2x + \\cos(x)]] or [[3.14]]", "ground_truth": {"f": "\\cos{\\left(x \\right)}", "g": "x^{3}", "problem_type": "evaluate", "correct_answer": 11.0907, "x_value": 2}}
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