mirror of
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64 lines
22 KiB
JSON
Executable file
64 lines
22 KiB
JSON
Executable file
{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -4★-3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -4, "b": -3, "operator": "★", "correct_answer": 5.102077496632204}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 1★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 1, "b": 3, "operator": "★", "correct_answer": 7.09861228866811}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -3◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -3, "b": 5, "operator": "◆", "correct_answer": 5.182195733396728}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute 0★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": 0, "b": 2, "operator": "★", "correct_answer": 2.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4◆-1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -1, "operator": "◆", "correct_answer": 4.613705638880109}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1x, compute 3◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1x", "a": 3, "b": 4, "operator": "◆", "correct_answer": 9.5}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -3●-2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -3, "b": -2, "operator": "●", "correct_answer": -10.25}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute -5◆3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": -5, "b": 3, "operator": "◆", "correct_answer": -18.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^4, compute -3◆3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^4", "a": -3, "b": 3, "operator": "◆", "correct_answer": 103.2}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -3●0.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -3, "b": 0, "operator": "●", "correct_answer": 4.010007503399555}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -3★-1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -3, "b": -1, "operator": "★", "correct_answer": 4.469705197531415}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 1◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 1, "b": 4, "operator": "◆", "correct_answer": 4.401726519884175}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5●-3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": -3, "operator": "●", "correct_answer": 4.8999557172769945}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -5●3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -5, "b": 3, "operator": "●", "correct_answer": 7.273654682063672}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5●-1.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": -1, "operator": "●", "correct_answer": 4.199604740528965}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, a★1 = 20. Find a.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "b", "known_value": 1, "target_var": "a", "operator": "★", "result": 20, "correct_answers": [1e-06]}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 2◆3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 2, "b": 3, "operator": "◆", "correct_answer": 6.573845660053303}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -3◆-2.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -3, "b": -2, "operator": "◆", "correct_answer": 5.594534891891835}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -3★0.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -3, "b": 0, "operator": "★", "correct_answer": 6.141120008059867}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -3◆0.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -3, "b": 0, "operator": "◆", "correct_answer": 4.010007503399555}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -4★2.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -4, "b": 2, "operator": "★", "correct_answer": -54.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -5★1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -5, "b": 1, "operator": "★", "correct_answer": -150.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, b●3 = 3. Find b.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "a", "known_value": 3, "target_var": "b", "operator": "●", "result": 3, "correct_answers": [0.149361]}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 1●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 1, "b": 4, "operator": "●", "correct_answer": 7.386294361119891}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -4★4.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -4, "b": 4, "operator": "★", "correct_answer": 6.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute 0★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": 0, "b": 3, "operator": "★", "correct_answer": -3.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -1★0.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -1, "b": 0, "operator": "★", "correct_answer": 6.841470984807897}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 3x, compute 2●3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "3x", "a": 2, "b": 3, "operator": "●", "correct_answer": 13.5}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -1x, compute -5●-2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-1x", "a": -5, "b": -2, "operator": "●", "correct_answer": 16.5}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -2◆-1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -2, "b": -1, "operator": "◆", "correct_answer": 6.067826442017785}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 0★3.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 0, "b": 3, "operator": "★", "correct_answer": 7.989992496600445}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4●-3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -3, "operator": "●", "correct_answer": 5.712317927548219}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, b★2 = 17. Find b.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "1/x", "known_var": "a", "known_value": 2, "target_var": "b", "operator": "★", "result": 17, "correct_answers": [119748.28343]}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 2x, a★4 = 6. Find a.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "2x", "known_var": "b", "known_value": 4, "target_var": "a", "operator": "★", "result": 6, "correct_answers": [-4.0, 4.0]}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 3●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 3, "b": 4, "operator": "●", "correct_answer": 5.102077496632204}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute 0●2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": 0, "b": 2, "operator": "●", "correct_answer": 6.909297426825682}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -5★-4.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -5, "b": -4, "operator": "★", "correct_answer": 5.77685644868579}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute -5★1.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": -5, "b": 1, "operator": "★", "correct_answer": 5.743359879595086}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 2◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 2, "b": 5, "operator": "◆", "correct_answer": 6.916290731874155}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute 4◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": 4, "b": 5, "operator": "◆", "correct_answer": -3.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 1◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 1, "b": 5, "operator": "◆", "correct_answer": 7.6094379124341005}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -4●-1.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -4, "b": -1, "operator": "●", "correct_answer": 4.613705638880109}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 2●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 2, "b": 5, "operator": "●", "correct_answer": 5.300190977989631}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1●4.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 4, "operator": "●", "correct_answer": 7.193945926731752}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -4●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -4, "b": 5, "operator": "●", "correct_answer": 4.2842732300289335}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 3●5.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 3, "b": 5, "operator": "●", "correct_answer": 6.5108256237659905}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 1◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 1, "b": 4, "operator": "◆", "correct_answer": 7.193945926731752}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, a●0 = 17. Find a.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^2", "known_var": "b", "known_value": 0, "target_var": "a", "operator": "●", "result": 17, "correct_answers": [-3.207534]}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -3●3.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -3, "b": 3, "operator": "●", "correct_answer": 6.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, compute -4◆2.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^3", "a": -4, "b": 2, "operator": "◆", "correct_answer": -54.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1x, compute -1★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1x", "a": -1, "b": 5, "operator": "★", "correct_answer": 18.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -2●0.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -2, "b": 0, "operator": "●", "correct_answer": 6.909297426825682}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute -2◆-1.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": -2, "b": -1, "operator": "◆", "correct_answer": 5.306852819440055}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -5◆-3.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -5, "b": -3, "operator": "◆", "correct_answer": 4.8999557172769945}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -3★0.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -3, "b": 0, "operator": "★", "correct_answer": 6.141120008059867}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute -1◆0.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": -1, "b": 0, "operator": "◆", "correct_answer": 7.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = cos(x), compute -4★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "cos(x)", "a": -4, "b": 5, "operator": "★", "correct_answer": 4.2842732300289335}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 3◆5.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 3, "b": 5, "operator": "◆", "correct_answer": 6.5108256237659905}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^2, compute 3◆4.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "x^2", "a": 3, "b": 4, "operator": "◆", "correct_answer": 18.333333333333332}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = sin(x), compute 0★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "sin(x)", "a": 0, "b": 5, "operator": "★", "correct_answer": 6.716337814536773}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 3★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 3, "b": 5, "operator": "★", "correct_answer": 6.5108256237659905}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = x^3, a◆-3 = 3. Find a.\nThe operation a◆b is defined as ∫_a^b f(x)dx + 6. For multiple answers, separate with 'or'. Use fractions if needed. Put your answer in [[ ]].", "ground_truth": {"problem_type": "solve", "f": "x^3", "known_var": "b", "known_value": -3, "target_var": "a", "operator": "◆", "result": 3, "correct_answers": [3.105423, -3.105423]}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = -2x, compute -5●2.\nThe operation a●b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "-2x", "a": -5, "b": 2, "operator": "●", "correct_answer": 27.0}}
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{"data_source": "KorOperationUnicode25cf", "prompt": "Given f(x) = 1/x, compute 3★5.\nThe operation a★b is defined as ∫_a^b f(x)dx + 6. Calculate the result. For fractions, use 'a/b' format. Put your answer in [[ ]].", "ground_truth": {"problem_type": "compute", "f": "1/x", "a": 3, "b": 5, "operator": "★", "correct_answer": 6.5108256237659905}}
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