question stringlengths 27 826 | answer stringlengths 1 110 | metadata stringlengths 205 342 | dataset_source stringclasses 6
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|---|---|---|---|
Subtract the complex numbers: (-10.0 - 2.0i) - (-3.0 - 3.0i) | -7.0 + 1.0i | {"source_dataset": "complex_arithmetic", "source_index": 0, "num1": [-10.0, -2.0], "num2": [-3.0, -3.0], "operation": "-", "result": [-7, 1], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (-6.0 + 4.0i) + (1.0 - 7.0i) | -5.0 - 3.0i | {"source_dataset": "complex_arithmetic", "source_index": 1, "num1": [-6.0, 4.0], "num2": [1.0, -7.0], "operation": "+", "result": [-5, -3], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Subtract the complex numbers: (7.0 - 7.0i) - (-5.0 + 2.0i) | 12.0 - 9.0i | {"source_dataset": "complex_arithmetic", "source_index": 2, "num1": [7.0, -7.0], "num2": [-5.0, 2.0], "operation": "-", "result": [12, -9], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (5.0 - 2.0i) + (-8.0 - 1.0i) | -3.0 - 3.0i | {"source_dataset": "complex_arithmetic", "source_index": 3, "num1": [5.0, -2.0], "num2": [-8.0, -1.0], "operation": "+", "result": [-3, -3], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Multiply the complex numbers: (2.0 - 9.0i) × (8.0 + 8.0i) | 88.0 - 56.0i | {"source_dataset": "complex_arithmetic", "source_index": 4, "num1": [2.0, -9.0], "num2": [8.0, 8.0], "operation": "*", "result": [88, -56], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (3.0 + 7.0i) + (4.0 + 8.0i) | 7.0 + 15.0i | {"source_dataset": "complex_arithmetic", "source_index": 5, "num1": [3.0, 7.0], "num2": [4.0, 8.0], "operation": "+", "result": [7, 15], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Subtract the complex numbers: (-6.0 + 7.0i) - (7.0 - 1.0i) | -13.0 + 8.0i | {"source_dataset": "complex_arithmetic", "source_index": 6, "num1": [-6.0, 7.0], "num2": [7.0, -1.0], "operation": "-", "result": [-13, 8], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (3.0 - 7.0i) + (7.00i) | 3.00 | {"source_dataset": "complex_arithmetic", "source_index": 7, "num1": [3.0, -7.0], "num2": [0.0, 7.0], "operation": "+", "result": [3, 0], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Subtract the complex numbers: (-2.0 + 1.0i) - (10.0 - 3.0i) | -12.0 + 4.0i | {"source_dataset": "complex_arithmetic", "source_index": 8, "num1": [-2.0, 1.0], "num2": [10.0, -3.0], "operation": "-", "result": [-12, 4], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (6.0 + 7.0i) + (-5.0 - 3.0i) | 1.0 + 4.0i | {"source_dataset": "complex_arithmetic", "source_index": 9, "num1": [6.0, 7.0], "num2": [-5.0, -3.0], "operation": "+", "result": [1, 4], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Divide the complex numbers: (-51.0 + 21.0i) ÷ (5.0 + 1.0i) | -9.0 + 6.0i | {"source_dataset": "complex_arithmetic", "source_index": 10, "num1": [-51.0, 21.0], "num2": [5.0, 1.0], "operation": "/", "result": [-9, 6], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Subtract the complex numbers: (-4.0 + 4.0i) - (6.0 + 5.0i) | -10.0 - 1.0i | {"source_dataset": "complex_arithmetic", "source_index": 11, "num1": [-4.0, 4.0], "num2": [6.0, 5.0], "operation": "-", "result": [-10, -1], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Divide the complex numbers: (-38.0 + 34.0i) ÷ (7.0 - 1.0i) | -6.0 + 4.0i | {"source_dataset": "complex_arithmetic", "source_index": 12, "num1": [-38.0, 34.0], "num2": [7.0, -1.0], "operation": "/", "result": [-6, 4], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (-4.0 - 6.0i) + (-1.0 - 8.0i) | -5.0 - 14.0i | {"source_dataset": "complex_arithmetic", "source_index": 13, "num1": [-4.0, -6.0], "num2": [-1.0, -8.0], "operation": "+", "result": [-5, -14], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Divide the complex numbers: (135.0 + 20.0i) ÷ (5.0 + 10.0i) | 7.0 - 10.0i | {"source_dataset": "complex_arithmetic", "source_index": 14, "num1": [135.0, 20.0], "num2": [5.0, 10.0], "operation": "/", "result": [7, -10], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (8.0 + 9.0i) + (-10.0 - 3.0i) | -2.0 + 6.0i | {"source_dataset": "complex_arithmetic", "source_index": 15, "num1": [8.0, 9.0], "num2": [-10.0, -3.0], "operation": "+", "result": [-2, 6], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Subtract the complex numbers: (-4.0 + 10.0i) - (-4.0 - 9.0i) | 19.00i | {"source_dataset": "complex_arithmetic", "source_index": 16, "num1": [-4.0, 10.0], "num2": [-4.0, -9.0], "operation": "-", "result": [0, 19], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (10.0 + 4.0i) + (-10.0 - 6.0i) | -2.00i | {"source_dataset": "complex_arithmetic", "source_index": 17, "num1": [10.0, 4.0], "num2": [-10.0, -6.0], "operation": "+", "result": [0, -2], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Add the complex numbers: (8.0 - 6.0i) + (-2.0 - 3.0i) | 6.0 - 9.0i | {"source_dataset": "complex_arithmetic", "source_index": 18, "num1": [8.0, -6.0], "num2": [-2.0, -3.0], "operation": "+", "result": [6, -9], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Subtract the complex numbers: (7.0 - 4.0i) - (-1.00i) | 7.0 - 3.0i | {"source_dataset": "complex_arithmetic", "source_index": 19, "num1": [7.0, -4.0], "num2": [0.0, -1.0], "operation": "-", "result": [7, -3], "difficulty": {"min_real": -10, "max_real": 10, "min_imag": -10, "max_imag": 10, "operations_weights": [0.4, 0.4, 0.1, 0.1]}} | complex_arithmetic |
Find the indefinite integral: ∫ (16*x + 4)*exp(4*x**2 + 2*x + 10) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multipli... | 2*exp(4*x**2 + 2*x + 10) + C | {"source_dataset": "intermediate_integration", "source_index": 0, "integrand": "(16*x + 4)*exp(4*x**2 + 2*x + 10)", "problem_type": "exponential", "variable": "x", "expected_answer_expression": "2*exp(4*x**2 + 2*x + 10)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Evaluate the indefinite integral: ∫ -3*(8*x + 6)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operati... | -384*x**4 - 1152*x**3 - 1296*x**2 - 648*x + C | {"source_dataset": "intermediate_integration", "source_index": 1, "integrand": "-3*(8*x + 6)**3", "problem_type": "linear", "variable": "x", "expected_answer_expression": "-384*x**4 - 1152*x**3 - 1296*x**2 - 648*x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Find the indefinite integral: ∫ -4*sin(4*x + 1)**2*cos(4*x + 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplica... | -sin(4*x + 1)**3/3 + C | {"source_dataset": "intermediate_integration", "source_index": 2, "integrand": "-4*sin(4*x + 1)**2*cos(4*x + 1)", "problem_type": "trigonometric", "variable": "x", "expected_answer_expression": "-sin(4*x + 1)**3/3", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Find the indefinite integral: ∫ -2*asin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in yo... | -2*x*asin(x) - 2*sqrt(1 - x**2) + C | {"source_dataset": "intermediate_integration", "source_index": 3, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "expected_answer_expression": "-2*x*asin(x) - 2*sqrt(1 - x**2)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Evaluate the indefinite integral: ∫ 3*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operation... | (3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C | {"source_dataset": "intermediate_integration", "source_index": 4, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "expected_answer_expression": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Calculate the antiderivative: ∫ -3*atan(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in ... | -3*x*atan(2*x) + 3*log(4*x**2 + 1)/4 + C | {"source_dataset": "intermediate_integration", "source_index": 5, "integrand": "-3*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "expected_answer_expression": "-3*x*atan(2*x) + 3*log(4*x**2 + 1)/4", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Evaluate the indefinite integral: ∫ 2*x**3*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operati... | 2*Integral(x**3*cos(3*x), x) + C | {"source_dataset": "intermediate_integration", "source_index": 6, "integrand": "2*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "expected_answer_expression": "2*Integral(x**3*cos(3*x), x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Find the indefinite integral: ∫ -(2*x + 6)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in... | -16*x**5/5 - 48*x**4 - 288*x**3 - 864*x**2 - 1296*x + C | {"source_dataset": "intermediate_integration", "source_index": 7, "integrand": "-(2*x + 6)**4", "problem_type": "linear", "variable": "x", "expected_answer_expression": "-16*x**5/5 - 48*x**4 - 288*x**3 - 864*x**2 - 1296*x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}... | intermediate_integration |
Find the indefinite integral: ∫ -8*sin(8*x - 2)*cos(8*x - 2)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplica... | cos(8*x - 2)**4/4 + C | {"source_dataset": "intermediate_integration", "source_index": 8, "integrand": "-8*sin(8*x - 2)*cos(8*x - 2)**3", "problem_type": "trigonometric", "variable": "x", "expected_answer_expression": "cos(8*x - 2)**4/4", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Evaluate the indefinite integral: ∫ -12*sqrt(4*x - 7) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication opera... | -2*(4*x - 7)**(3/2) + C | {"source_dataset": "intermediate_integration", "source_index": 9, "integrand": "-12*sqrt(4*x - 7)", "problem_type": "radical", "variable": "x", "expected_answer_expression": "-2*(4*x - 7)**(3/2)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Find the indefinite integral: ∫ 2*x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in... | 2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C | {"source_dataset": "intermediate_integration", "source_index": 10, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "expected_answer_expression": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0... | intermediate_integration |
Evaluate the indefinite integral: ∫ -2*x**2*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operat... | -2*Integral(x**2*cos(3*x), x) + C | {"source_dataset": "intermediate_integration", "source_index": 11, "integrand": "-2*x**2*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "expected_answer_expression": "-2*Integral(x**2*cos(3*x), x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Calculate the antiderivative: ∫ -2*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations i... | (-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C | {"source_dataset": "intermediate_integration", "source_index": 12, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "expected_answer_expression": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Find the indefinite integral: ∫ -(3*x + 5)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in... | -81*x**5/5 - 135*x**4 - 450*x**3 - 750*x**2 - 625*x + C | {"source_dataset": "intermediate_integration", "source_index": 13, "integrand": "-(3*x + 5)**4", "problem_type": "linear", "variable": "x", "expected_answer_expression": "-81*x**5/5 - 135*x**4 - 450*x**3 - 750*x**2 - 625*x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]... | intermediate_integration |
Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operatio... | (-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C | {"source_dataset": "intermediate_integration", "source_index": 14, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "expected_answer_expression": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Evaluate the indefinite integral: ∫ -2*(4*x - 9)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operati... | -32*x**4 + 288*x**3 - 972*x**2 + 1458*x + C | {"source_dataset": "intermediate_integration", "source_index": 15, "integrand": "-2*(4*x - 9)**3", "problem_type": "linear", "variable": "x", "expected_answer_expression": "-32*x**4 + 288*x**3 - 972*x**2 + 1458*x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Calculate the antiderivative: ∫ x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in y... | Integral(x**3*cos(x), x) + C | {"source_dataset": "intermediate_integration", "source_index": 16, "integrand": "x**3*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "expected_answer_expression": "Integral(x**3*cos(x), x)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Calculate the antiderivative: ∫ 9*sqrt(3*x - 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations ... | 2*(3*x - 1)**(3/2) + C | {"source_dataset": "intermediate_integration", "source_index": 17, "integrand": "9*sqrt(3*x - 1)", "problem_type": "radical", "variable": "x", "expected_answer_expression": "2*(3*x - 1)**(3/2)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Calculate the antiderivative: ∫ -2*asin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in yo... | -2*x*asin(x) - 2*sqrt(1 - x**2) + C | {"source_dataset": "intermediate_integration", "source_index": 18, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "expected_answer_expression": "-2*x*asin(x) - 2*sqrt(1 - x**2)", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Calculate the antiderivative: ∫ -12*sin(6*x - 8)*cos(6*x - 8)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplic... | cos(6*x - 8)**4/2 + C | {"source_dataset": "intermediate_integration", "source_index": 19, "integrand": "-12*sin(6*x - 8)*cos(6*x - 8)**3", "problem_type": "trigonometric", "variable": "x", "expected_answer_expression": "cos(6*x - 8)**4/2", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}} | intermediate_integration |
Find the real value(s) of w in the equation: -127*w = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), conv... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 0, "polynomial_expr": "-127*w", "variable": "w", "degree": 1, "real_solutions": [0.0], "num_terms": 2, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Determine the real value(s) of b that satisfies: 86*b**2 - 2*b - 13 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4... | -0.3773, 0.4006 | {"source_dataset": "polynomial_equations", "source_index": 1, "polynomial_expr": "86*b**2 - 2*b - 13", "variable": "b", "degree": 2, "real_solutions": [-0.3773, 0.4006], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Determine the real value(s) of p that satisfies: 71*p**3 - 2*p - 29 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4... | 0.7546 | {"source_dataset": "polynomial_equations", "source_index": 2, "polynomial_expr": "71*p**3 - 2*p - 29", "variable": "p", "degree": 3, "real_solutions": [0.7546], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real d: 98 - 94*d**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal f... | -1.0211, 1.0211 | {"source_dataset": "polynomial_equations", "source_index": 3, "polynomial_expr": "98 - 94*d**2", "variable": "d", "degree": 2, "real_solutions": [-1.0211, 1.0211], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real c: 106*c**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form ... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 4, "polynomial_expr": "106*c**2", "variable": "c", "degree": 2, "real_solutions": [0.0], "num_terms": 2, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Find the real value(s) of n in the equation: 138*n = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), conve... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 5, "polynomial_expr": "138*n", "variable": "n", "degree": 1, "real_solutions": [0.0], "num_terms": 3, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve the polynomial equation for real t:
27*t**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), conver... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 6, "polynomial_expr": "27*t**2", "variable": "t", "degree": 2, "real_solutions": [0.0], "num_terms": 2, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real c: 97*c**2 + 98*c + 7 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to dec... | -0.933, -0.0774 | {"source_dataset": "polynomial_equations", "source_index": 7, "polynomial_expr": "97*c**2 + 98*c + 7", "variable": "c", "degree": 2, "real_solutions": [-0.933, -0.0774], "num_terms": 3, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Find the real value(s) of t in the equation: -28*t = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), conve... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 8, "polynomial_expr": "-28*t", "variable": "t", "degree": 1, "real_solutions": [0.0], "num_terms": 2, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Determine the real value(s) of h that satisfies: -71*h**3 + 182*h = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(456... | -1.6011, 0.0, 1.6011 | {"source_dataset": "polynomial_equations", "source_index": 9, "polynomial_expr": "-71*h**3 + 182*h", "variable": "h", "degree": 3, "real_solutions": [-1.6011, 0.0, 1.6011], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Find the real value(s) of k in the equation: 34*k = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), conver... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 10, "polynomial_expr": "34*k", "variable": "k", "degree": 1, "real_solutions": [0.0], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Determine the real value(s) of v that satisfies: -85*v = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), c... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 11, "polynomial_expr": "-85*v", "variable": "v", "degree": 1, "real_solutions": [0.0], "num_terms": 3, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Find the real value(s) of e in the equation: -49*e**2 + 119*e = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/1... | 0.0, 2.4286 | {"source_dataset": "polynomial_equations", "source_index": 12, "polynomial_expr": "-49*e**2 + 119*e", "variable": "e", "degree": 2, "real_solutions": [0.0, 2.4286], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve the polynomial equation for real c:
-28*c = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert ... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 13, "polynomial_expr": "-28*c", "variable": "c", "degree": 1, "real_solutions": [0.0], "num_terms": 2, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real t: t = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form in your... | 0.0 | {"source_dataset": "polynomial_equations", "source_index": 14, "polynomial_expr": "t", "variable": "t", "degree": 1, "real_solutions": [0.0], "num_terms": 3, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real b: 7 - 128*b**2 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal f... | -0.2339, 0.2339 | {"source_dataset": "polynomial_equations", "source_index": 15, "polynomial_expr": "7 - 128*b**2", "variable": "b", "degree": 2, "real_solutions": [-0.2339, 0.2339], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Determine the real value(s) of u that satisfies: -6*u - 52 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"... | -8.6667 | {"source_dataset": "polynomial_equations", "source_index": 16, "polynomial_expr": "-6*u - 52", "variable": "u", "degree": 1, "real_solutions": [-8.6667], "num_terms": 2, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real h: 127*h - 132 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal fo... | 1.0394 | {"source_dataset": "polynomial_equations", "source_index": 17, "polynomial_expr": "127*h - 132", "variable": "h", "degree": 1, "real_solutions": [1.0394], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real l: -62*l**2 + 6*l + 55 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to de... | -0.8947, 0.9915 | {"source_dataset": "polynomial_equations", "source_index": 18, "polynomial_expr": "-62*l**2 + 6*l + 55", "variable": "l", "degree": 2, "real_solutions": [-0.8947, 0.9915], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Solve for real r: -64*r - 4 = 0
In solving equations, please follow these instructions:
1. Provide all answers as comma-separated decimal values. For example: "-0.3773, 0.4005"
2. For solutions that can be expressed in exact form (like "u = 2 + sqrt(4560)/172" and "u = 2 - sqrt(4560)/172"), convert them to decimal form... | -0.0625 | {"source_dataset": "polynomial_equations", "source_index": 19, "polynomial_expr": "-64*r - 4", "variable": "r", "degree": 1, "real_solutions": [-0.0625], "num_terms": 4, "difficulty": {"terms": [2, 4], "degree": [1, 3]}} | polynomial_equations |
Calculate the following: (18 - 95*z**2)*(-104*z**3 - 12*z + 78)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, ... | 9880*z**5 - 732*z**3 - 7410*z**2 - 216*z + 1404 | {"source_dataset": "polynomial_multiplication", "source_index": 0, "polynomial_expr": "(18 - 95*z**2)*(-104*z**3 - 12*z + 78)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (74*x**2 + 16*x + 98)*(77*x**2 - 49*x + 8)*(-163*x**3 + 8*x - 49)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your re... | -928774*x**7 + 390222*x**6 - 1153118*x**5 + 463508*x**4 + 48346*x**3 - 397738*x**2 + 235298*x - 38416 | {"source_dataset": "polynomial_multiplication", "source_index": 1, "polynomial_expr": "(74*x**2 + 16*x + 98)*(77*x**2 - 49*x + 8)*(-163*x**3 + 8*x - 49)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_pol... | polynomial_multiplication |
Calculate the following: (29 - 49*y**2)*(21*y**3 + 49*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `... | -1029*y**5 - 1792*y**3 + 1421*y | {"source_dataset": "polynomial_multiplication", "source_index": 2, "polynomial_expr": "(29 - 49*y**2)*(21*y**3 + 49*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (74 - 123*y**3)*(96 - 104*y**2)*(15*y**3 - 36)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For ... | 191880*y**8 - 177120*y**6 - 575952*y**5 + 531648*y**3 + 277056*y**2 - 255744 | {"source_dataset": "polynomial_multiplication", "source_index": 3, "polynomial_expr": "(74 - 123*y**3)*(96 - 104*y**2)*(15*y**3 - 36)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Calculate the following: (76 - 20*x)*(18*x**2 - 11*x)*(44*x**3 - 62*x**2 - 150*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning st... | -15840*x**6 + 92192*x**5 - 81240*x**4 - 186368*x**3 + 125400*x**2 | {"source_dataset": "polynomial_multiplication", "source_index": 4, "polynomial_expr": "(76 - 20*x)*(18*x**2 - 11*x)*(44*x**3 - 62*x**2 - 150*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials"... | polynomial_multiplication |
Calculate the following: 44*y*(y**3 + 62)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) ... | 44*y**4 + 2728*y | {"source_dataset": "polynomial_multiplication", "source_index": 5, "polynomial_expr": "44*y*(y**3 + 62)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Calculate the following: (51*z - 85)*(72*z**2 + 65*z)*(17*z**3 - 66*z + 13)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. F... | 62424*z**6 - 47685*z**5 - 336277*z**4 + 232866*z**3 + 328185*z**2 - 71825*z | {"source_dataset": "polynomial_multiplication", "source_index": 6, "polynomial_expr": "(51*z - 85)*(72*z**2 + 65*z)*(17*z**3 - 66*z + 13)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (-83*x**2 + 66*x)*(-42*x**2 + 52*x + 89)*(78*x**2 - 70*x + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reason... | 271908*x**6 - 796884*x**5 + 208586*x**4 + 692494*x**3 - 434910*x**2 + 35244*x | {"source_dataset": "polynomial_multiplication", "source_index": 7, "polynomial_expr": "(-83*x**2 + 66*x)*(-42*x**2 + 52*x + 89)*(78*x**2 - 70*x + 6)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynom... | polynomial_multiplication |
Calculate the following: -25*y**3*(-99*y**3 + 123*y**2)*(9*y**3 + 43*y)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For e... | 22275*y**9 - 27675*y**8 + 106425*y**7 - 132225*y**6 | {"source_dataset": "polynomial_multiplication", "source_index": 8, "polynomial_expr": "-25*y**3*(-99*y**3 + 123*y**2)*(9*y**3 + 43*y)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (51*x**3 + 30*x**2)*(47*x**3 + 64*x**2 + 52*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For ... | 2397*x**6 + 4674*x**5 + 4572*x**4 + 1560*x**3 | {"source_dataset": "polynomial_multiplication", "source_index": 9, "polynomial_expr": "(51*x**3 + 30*x**2)*(47*x**3 + 64*x**2 + 52*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (71*y**2 + 18*y)*(-9*y**2 - 50*y - 81)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example,... | -639*y**4 - 3712*y**3 - 6651*y**2 - 1458*y | {"source_dataset": "polynomial_multiplication", "source_index": 10, "polynomial_expr": "(71*y**2 + 18*y)*(-9*y**2 - 50*y - 81)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Calculate the following: (22*z**2 - 34)*(65*z**3 + 67*z**2 + 94)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example,... | 1430*z**5 + 1474*z**4 - 2210*z**3 - 210*z**2 - 3196 | {"source_dataset": "polynomial_multiplication", "source_index": 11, "polynomial_expr": "(22*z**2 - 34)*(65*z**3 + 67*z**2 + 94)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (-2*x**2 - 106*x)*(19*x**3 - 27)*(150*x**2 + 58*x - 35)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning st... | -5700*x**7 - 304304*x**6 - 115482*x**5 + 78590*x**4 + 432432*x**3 + 164106*x**2 - 100170*x | {"source_dataset": "polynomial_multiplication", "source_index": 12, "polynomial_expr": "(-2*x**2 - 106*x)*(19*x**3 - 27)*(150*x**2 + 58*x - 35)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials"... | polynomial_multiplication |
Simplify this expression: (95*x**2 - 96)*(43*x**3 + 55*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write ... | 4085*x**5 + 1097*x**3 - 5280*x | {"source_dataset": "polynomial_multiplication", "source_index": 13, "polynomial_expr": "(95*x**2 - 96)*(43*x**3 + 55*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: -223*z*(84*z**2 - 54*z - 80)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3... | -18732*z**3 + 12042*z**2 + 17840*z | {"source_dataset": "polynomial_multiplication", "source_index": 14, "polynomial_expr": "-223*z*(84*z**2 - 54*z - 80)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: 53*x**3*(83 - 16*x**3)*(-98*x**3 - 78*x + 95)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For e... | 83104*x**9 + 66144*x**7 - 511662*x**6 - 343122*x**4 + 417905*x**3 | {"source_dataset": "polynomial_multiplication", "source_index": 15, "polynomial_expr": "53*x**3*(83 - 16*x**3)*(-98*x**3 - 78*x + 95)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Calculate the following: (-58*z**3 - 95*z)*(34*z**3 + 54*z**2 - 14)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For examp... | -1972*z**6 - 3132*z**5 - 3230*z**4 - 4318*z**3 + 1330*z | {"source_dataset": "polynomial_multiplication", "source_index": 16, "polynomial_expr": "(-58*z**3 - 95*z)*(34*z**3 + 54*z**2 - 14)", "variables": ["z"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (75*x**2 + 20*x)*(-2*x**3 + 69*x**2 - 20*x)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For exa... | -150*x**5 + 5135*x**4 - 120*x**3 - 400*x**2 | {"source_dataset": "polynomial_multiplication", "source_index": 17, "polynomial_expr": "(75*x**2 + 20*x)*(-2*x**3 + 69*x**2 - 20*x)", "variables": ["x"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Simplify this expression: (-93*y**2 - 82)*(-14*y**3 + 8*y**2 + 72)*(-20*y**3 - 24*y**2 + 62*y + 6)
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in ... | -26040*y**8 - 16368*y**7 + 75620*y**6 + 81172*y**5 + 243160*y**4 - 330856*y**3 + 97584*y**2 - 366048*y - 35424 | {"source_dataset": "polynomial_multiplication", "source_index": 18, "polynomial_expr": "(-93*y**2 - 82)*(-14*y**3 + 8*y**2 + 72)*(-20*y**3 - 24*y**2 + 62*y + 6)", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, ... | polynomial_multiplication |
Simplify this expression: -588*y**3 - 903*y**2 - 2835
When performing calculations, please follow these guidelines:
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*... | -588*y**3 - 903*y**2 - 2835 | {"source_dataset": "polynomial_multiplication", "source_index": 19, "polynomial_expr": "-588*y**3 - 903*y**2 - 2835", "variables": ["y"], "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "min_degree": 0, "max_degree": 3, "min_polynomials": 2, "max_polynomials": 3}} | polynomial_multiplication |
Find the value of u in the equation: 32*u + 4 = 3044 | 95 | {"source_dataset": "simple_equations", "source_index": 0, "equation": "32*u + 4 = 3044", "variable": "u", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Determine the value of b that satisfies: 71 - 48*b = -2761 | 59 | {"source_dataset": "simple_equations", "source_index": 1, "equation": "71 - 48*b = -2761", "variable": "b", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of n in the equation: 175 - 29*n = -202 | 13 | {"source_dataset": "simple_equations", "source_index": 2, "equation": "175 - 29*n = -202", "variable": "n", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for i: 44*i + 52 = 712 | 15 | {"source_dataset": "simple_equations", "source_index": 3, "equation": "44*i + 52 = 712", "variable": "i", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of c in the equation: 82*c - 152 = 258 | 5 | {"source_dataset": "simple_equations", "source_index": 4, "equation": "82*c - 152 = 258", "variable": "c", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for l: 74*l + 56 = 4940 | 66 | {"source_dataset": "simple_equations", "source_index": 5, "equation": "74*l + 56 = 4940", "variable": "l", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for r: -39*r - 55 = -3643 | 92 | {"source_dataset": "simple_equations", "source_index": 6, "equation": "-39*r - 55 = -3643", "variable": "r", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Determine the value of c that satisfies: 795 - 66*c = -5673 | 98 | {"source_dataset": "simple_equations", "source_index": 7, "equation": "795 - 66*c = -5673", "variable": "c", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for p: 61*p - 35 = 4174 | 69 | {"source_dataset": "simple_equations", "source_index": 8, "equation": "61*p - 35 = 4174", "variable": "p", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Determine the value of h that satisfies: 20 - 51*h = -3448 | 68 | {"source_dataset": "simple_equations", "source_index": 9, "equation": "20 - 51*h = -3448", "variable": "h", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of i in the equation: 93 - 48*i = -771 | 18 | {"source_dataset": "simple_equations", "source_index": 10, "equation": "93 - 48*i = -771", "variable": "i", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for t: 59 - 92*t = -8589 | 94 | {"source_dataset": "simple_equations", "source_index": 11, "equation": "59 - 92*t = -8589", "variable": "t", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for e: 49*e + 134 = 4740 | 94 | {"source_dataset": "simple_equations", "source_index": 12, "equation": "49*e + 134 = 4740", "variable": "e", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of c in the equation: 20 - 11*c = -409 | 39 | {"source_dataset": "simple_equations", "source_index": 13, "equation": "20 - 11*c = -409", "variable": "c", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Determine the value of r that satisfies: 61 - 99*r = -5285 | 54 | {"source_dataset": "simple_equations", "source_index": 14, "equation": "61 - 99*r = -5285", "variable": "r", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Determine the value of b that satisfies: 66*b + 75 = 3771 | 56 | {"source_dataset": "simple_equations", "source_index": 15, "equation": "66*b + 75 = 3771", "variable": "b", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Solve for s: 6*s + 95 = 407 | 52 | {"source_dataset": "simple_equations", "source_index": 16, "equation": "6*s + 95 = 407", "variable": "s", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of h in the equation: 1062*h = 97704 | 92 | {"source_dataset": "simple_equations", "source_index": 17, "equation": "1062*h = 97704", "variable": "h", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of j in the equation: 62*j + 14 = 386 | 6 | {"source_dataset": "simple_equations", "source_index": 18, "equation": "62*j + 14 = 386", "variable": "j", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
Find the value of p in the equation: 38*p + 72 = 3454 | 89 | {"source_dataset": "simple_equations", "source_index": 19, "equation": "38*p + 72 = 3454", "variable": "p", "difficulty": {"min_terms": 2, "max_terms": 4, "min_value": 1, "max_value": 100, "operators_weights": [0.4, 0.4, 0.2]}} | simple_equations |
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