{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2sin(1\u03c0x - 2) + 2) - 2| + 2, g(x) = 4x^2 + 1x - 5, x = -1.4, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(3\u03c0(3x - 2) + 2) + 1, g(x) = -2x^2 + 2x + 4, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1e^(-1x) - 2) - 1)/(-3(-1e^(-1x) - 2) - 3) and g(x) = -3|x + 1| + 3 between the vertical lines x = -2.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-4x^2 - 5x + 5) - 1 and g(x) = -2x - 4 from x = -2.0 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1cos(1\u03c0x - 2) + 1) + 5, g(x) = 2|x + 2| - 1, x = -4.1, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4x^2 + 1x) - 3 and g(x) = -4x^2 - 5x - 4 between the vertical lines x = -0.2 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(3sin(1\u03c0x + 3) + 1) - 2)/(-2(3sin(1\u03c0x + 3) + 1) + 3) and g(x) = 1|x + 2| - 1 between the vertical lines x = 3.1 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2cos(3\u03c0x - 2) + 2) + 4, g(x) = -2x + 2, x = -3.0, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2\u03c0(-2|x - 1|) - 2) - 1 and g(x) = (-2x + 3)/(-3x) between the vertical lines x = 4.4 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0(-3|x - 3| + 3)), g(x) = (-2x + 3)/(-2x - 2), x = 2.4, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(1\u03c0(1|x + 3| + 2)) - 3 and g(x) = 4x^2 + 4x - 5 from x = -1.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((-2x + 2)/(2x - 1)) + 1| and g(x) = 2|x - 2| - 1 from x = 1.9 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-4x^2 + 3x - 3) - 1)/(1(-4x^2 + 3x - 3) - 2) and g(x) = -2|x - 2| + 2 between the vertical lines x = 0.8 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0(-3x^2 + 1) + 3) + 2, g(x) = -1x - 3, x = -2.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1\u03c0((2x - 2)/(1x)) + 3) - 1 and g(x) = 5x + 3 between the vertical lines x = -0.4 and x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(-1x^2 - 5x + 1) + 3) + 1 and g(x) = 1x - 4 from x = 4.5 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-1x^2 + 3x - 1)^2 + 1(-1x^2 + 3x - 1), g(x) = -1x + 3, x = 0.0, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(5x^2 - 3x + 4) - 1)/(-2(5x^2 - 3x + 4) - 1) and g(x) = -2x^2 + 1x + 4 from x = -1.3 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3((2x - 2)/(1x)) + 3)/(2((2x - 2)/(1x)) - 1), g(x) = (-1x + 1)/(2x + 2), x = -0.6, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-1x - 2)/(2x + 2)) - 3| + 3 and g(x) = 1x - 2 between the vertical lines x = -1.4 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(1|x - 3| + 2))/(3(1|x - 3| + 2) + 1), g(x) = -3x^2 + 2x + 2, x = -0.5, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((1x + 2)/(2x + 3)) - 3 and g(x) = -3x^2 + 4x + 3 from x = -1.5 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(2\u03c0x - 2) - 3)^2 + 1(-2sin(2\u03c0x - 2) - 3) and g(x) = 2x from x = -3.7 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1x^2 - 4x + 2)^2 + 3(-1x^2 - 4x + 2) - 5, g(x) = -2|x - 2| - 3, x = 0.2, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0(-5x + 4) - 2) and g(x) = 1|x + 2| from x = -2.1 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(1\u03c0x) + 3) + 2 and g(x) = 1x between the vertical lines x = -0.2 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(3x^2 - 2x - 4)^2 + 1(3x^2 - 2x - 4) + 2 and g(x) = (2x)/(2x + 2) from x = 1.4 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2sin(2\u03c0x + 2) - 2) + 5 and g(x) = 2x^2 + 3x + 3 from x = -2.3 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0(-1x^2 - 5x + 3) - 3) - 3, g(x) = -3x^2 + 5x + 2, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(2|x + 1| - 2) - 1 and g(x) = -4x - 4 from x = -1.6 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-3x - 3)) - 1 and g(x) = (-2x - 3)/(1x + 3) between the vertical lines x = -0.6 and x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0(3x - 2) - 1) + 3 and g(x) = -4x - 5 from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-4x^2 + 2x - 1) - 1 and g(x) = 2x - 4 from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(3\u03c0x) - 1)^2 + 4(1sin(3\u03c0x) - 1) + 1 and g(x) = -4x^2 + 2x from x = 0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-3x^2 + 1)| - 1 and g(x) = 3x^2 - 5x + 2 from x = -2.4 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1cos(3\u03c0x - 1)) + 2 and g(x) = 2x + 3 from x = -0.8 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1(-2x^2 + 5x + 5)) + 2 and g(x) = -2|x - 3| + 2 from x = -1.0 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-1sin(3\u03c0x - 1) + 2)| + 3, g(x) = -2x + 1, x = -1.9, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(3\u03c0(-1x^2 + 3x - 4) + 2) + 2, g(x) = (1x)/(3x + 2), x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(3\u03c0(4x + 3) - 2) + 2, g(x) = 5x^2 + 2x - 1, x = 0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(-1x + 2) - 2) + 1 and g(x) = (2x - 1)/(2x + 2) between the vertical lines x = 2.4 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0(2|x + 2| + 2) - 3) - 3, g(x) = -2x - 3, x = 0.6, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-2x - 1)/(-3x - 2)) + 3 and g(x) = 2|x + 3| from x = -1.0 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(2\u03c0(4x^2 - 5x + 5)) + 2 and g(x) = -5x + 2 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3cos(1\u03c0x - 1) + 1) + 3| - 2 and g(x) = 4x + 5 from x = -4.3 to x = -3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3cos(2\u03c0x)) + 3| - 1, g(x) = 1x^2 - 3, x = 2.3, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(1x - 4) - 1) + 3 and g(x) = (1x - 3)/(1x + 1) between the vertical lines x = -3.2 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(3cos(3\u03c0x + 3)) + 2)/(-3(3cos(3\u03c0x + 3)) - 1), g(x) = -1|x + 3| + 1, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((1x + 2)/(3x + 2))^2 - 5((1x + 2)/(3x + 2)) - 3, g(x) = -1x, x = -1.0, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-3sin(1\u03c0x + 2) + 2) - 4 and g(x) = (2x)/(-1x - 2) from x = 1.7 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-5x^2 + 2x + 1)^2 - 3(-5x^2 + 2x + 1) + 1, g(x) = (1x + 1)/(3x + 2), x = -0.3, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(1x^2 - 5x + 2)^2 + 4 and g(x) = 1|x| + 2 from x = 0.3 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1x - 1) and g(x) = -4x^2 + 3x + 5 between the vertical lines x = -0.6 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(2cos(3\u03c0x + 3) - 2) - 3)/(-2(2cos(3\u03c0x + 3) - 2) - 1), g(x) = (-2x + 1)/(-2x + 3), x = 1.1, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3sin(2\u03c0x + 2) - 3) + 2)/(-2(-3sin(2\u03c0x + 2) - 3) - 3) and g(x) = 2|x| between the vertical lines x = 3.3 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1x + 2)/(-3x - 1))^2 + 1((1x + 2)/(-3x - 1)) + 5 and g(x) = 3|x + 2| + 2 between the vertical lines x = -3.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(2x^2 + 4x - 1) + 2)/(3(2x^2 + 4x - 1)) and g(x) = 3x - 2 from x = 0.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1cos(2\u03c0x + 1) + 1) + 3)/(-2(1cos(2\u03c0x + 1) + 1) + 3) and g(x) = -1x - 5 from x = 4.0 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2e^(1(-1|x + 3| + 3)) + 1 and g(x) = 3|x| - 3 from x = -0.4 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(1x^2 - 5x + 1) - 1)/(-2(1x^2 - 5x + 1)), g(x) = -1|x + 2| - 3, x = 0.2, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-3x^2 + 3x + 4) - 3) + 3, g(x) = -2x - 1, x = -2.4, and x = -2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(1\u03c0x + 3)) + 1)/(-3(-3cos(1\u03c0x + 3)) + 2) and g(x) = -3x^2 - 1x + 1 between the vertical lines x = -3.5 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3cos(3\u03c0x) - 1) + 2)/(-3(-3cos(3\u03c0x) - 1) - 1) and g(x) = -1x^2 + 5x + 5 between the vertical lines x = -2.5 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1x - 5) + 2)/(-2(-1x - 5) - 1) and g(x) = 3|x - 3| - 3 from x = 2.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(2cos(2\u03c0x - 1) - 2) - 1)/(3(2cos(2\u03c0x - 1) - 2) + 1) and g(x) = -4x + 1 from x = -3.9 to x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-3x + 2)/(3x - 1))| - 1 and g(x) = -3|x - 2| + 2 from x = 1.2 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0((3x + 1)/(2x + 3)) - 3) - 2, g(x) = (-1x)/(1x - 3), x = -1.3, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-4x^2 + 3x + 3) - 1)/(3(-4x^2 + 3x + 3) - 2), g(x) = 3|x + 1| + 1, x = -0.5, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(3\u03c0(2x^2 - 5x) - 1) and g(x) = 4x^2 - 4x - 4 from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1|x - 2| - 1) + 3)/(3(1|x - 2| - 1) + 2), g(x) = -1|x| - 3, x = 1.9, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2x + 2) and g(x) = (-1x + 3)/(2x - 1) from x = -0.6 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1\u03c0(-1x^2 + 1)) - 3 and g(x) = 1x - 4 between the vertical lines x = 2.0 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1cos(2\u03c0x + 1) + 3) - 1| and g(x) = 2x^2 - 5x between the vertical lines x = -0.4 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(3cos(3\u03c0x + 3) + 2) - 3)/(1(3cos(3\u03c0x + 3) + 2)), g(x) = (2x + 3)/(3x + 1), x = 2.2, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(2\u03c0x - 2)) + 1 and g(x) = -5x^2 - 3x + 3 between the vertical lines x = -1.1 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(3x^2 + 1x) + 2 and g(x) = 3x between the vertical lines x = -0.9 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2x^2 - 1x + 3) - 2 and g(x) = -1x^2 - 2x + 2 from x = -2.1 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(3\u03c0(-1x^2 - 4x)) - 2 and g(x) = (3x + 1)/(-1x + 2) from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-1cos(3\u03c0x - 3) + 3) + 2)/(1(-1cos(3\u03c0x - 3) + 3) - 2), g(x) = -3x + 1, x = 2.5, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2|x - 2| + 3) - 3)/(-3(-2|x - 2| + 3) - 1), g(x) = 1x + 2, x = 0.5, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-2x - 2)/(-2x)) - 5 and g(x) = 1x - 2 from x = -3.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2cos(2\u03c0x + 2) + 1) + 3)/(-1(-2cos(2\u03c0x + 2) + 1) + 2), g(x) = 5x^2 - 1x, x = -1.6, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2\u03c0(2x + 4) + 2) + 1 and g(x) = 3x^2 + 5x - 2 between the vertical lines x = -2.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-3cos(3\u03c0x - 2) + 2) + 2 and g(x) = 3x + 2 from x = -1.1 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2e^(2x)) + 3)/(-1(-2e^(2x)) + 2) and g(x) = (1x + 3)/(-3x + 2) between the vertical lines x = -0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1sin(3\u03c0x - 3) + 1)^2 - 4(-1sin(3\u03c0x - 3) + 1) + 2, g(x) = -1x + 1, x = 0.6, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2|x| - 1) - 1)/(-2(-2|x| - 1) + 3) and g(x) = -3|x - 3| + 2 between the vertical lines x = 2.6 and x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(2\u03c0(-4x^2 - 4x + 4) + 1) + 2 and g(x) = -2x - 5 from x = -3.1 to x = -3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1(3|x - 3| + 3)) + 1, g(x) = -2x^2 + 4x, x = 0.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((3x + 1)/(-1x + 3)) - 1 and g(x) = 3|x| - 3 from x = -1.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(3\u03c0(-1x - 2) - 3), g(x) = -4x + 3, x = 0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(2\u03c0(2|x + 3| + 2) - 2) + 2 and g(x) = 1x - 2 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((-2x - 1)/(-1x)) + 1)/(3((-2x - 1)/(-1x)) - 2) and g(x) = (-3x - 1)/(1x + 1) from x = -0.7 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-2sin(2\u03c0x + 1) + 3)^2 + 2(-2sin(2\u03c0x + 1) + 3) + 3 and g(x) = -1x^2 + 2x + 5 from x = 3.9 to x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(2|x - 3| - 1)^2 - 3(2|x - 3| - 1) + 3 and g(x) = -3x + 3 between the vertical lines x = 2.0 and x = 4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(3\u03c0(-5x^2 + 1x - 3) - 2) - 3 and g(x) = -5x^2 - 2x + 3 from x = 0.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2e^(1x) - 3) - 1| + 1 and g(x) = -5x^2 - 5x + 3 between the vertical lines x = 0.5 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3e^(1x) + 3) - 4 and g(x) = 1x + 2 between the vertical lines x = -2.8 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(2|x - 3| + 2) - 3), g(x) = 1x + 3, x = -1.3, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((3x + 2)/(2x - 3))^2 - 5 and g(x) = (-1x + 3)/(-3x - 1) from x = -0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(4x^2 - 1x - 2) + 3| - 3 and g(x) = -2|x| + 2 between the vertical lines x = -0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0(1x^2 + 2x + 3)) - 3 and g(x) = -4x between the vertical lines x = 0.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((-3x - 1)/(2x + 3)) - 2| + 1, g(x) = (1x + 1)/(-2x + 3), x = -1.0, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2cos(3\u03c0x + 2)) + 1)/(-2(-2cos(3\u03c0x + 2))) and g(x) = -3x^2 - 1x - 5 from x = 0.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2x)^2 + 5(2x) + 4 and g(x) = -1|x + 1| + 1 from x = -2.0 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2x + 4) - 1| + 1 and g(x) = 1|x + 3| + 3 between the vertical lines x = -2.2 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(3\u03c0(2|x - 2| - 1) + 1) - 3, g(x) = 1x - 4, x = -0.9, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((1x + 2)/(1x + 1)) + 2)/(1((1x + 2)/(1x + 1)) - 2) and g(x) = 1x + 2 from x = -4.0 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0((-1x)/(-3x - 3)) - 2) - 1 and g(x) = 1x - 2 from x = -0.7 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1\u03c0(5x - 3) + 1) - 2 and g(x) = (-1x + 1)/(2x - 1) between the vertical lines x = 0.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-3x)^2 + 3(-3x) + 1 and g(x) = 4x - 3 from x = -0.7 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(2x^2 + 2x - 3) + 1)/(-3(2x^2 + 2x - 3) + 4), g(x) = -1x - 5, x = -2.0, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(5x^2 - 4x + 1)^2 - 1(5x^2 - 4x + 1) and g(x) = 2x between the vertical lines x = 0.2 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-2sin(2\u03c0x - 2) + 2)^2 + 5(-2sin(2\u03c0x - 2) + 2) - 1 and g(x) = 3|x + 1| - 3 from x = -1.7 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0((-3x)/(2x - 1)) + 3) - 2, g(x) = 5x - 4, x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-3sin(1\u03c0x + 1) - 2)^2 + 5(-3sin(1\u03c0x + 1) - 2) + 2 and g(x) = -5x from x = -4.2 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(-2x + 1) + 3) - 3 and g(x) = -1|x + 1| - 1 from x = -3.6 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(2(-4x^2 + 3x + 4)) + 2 and g(x) = 1|x - 2| - 2 from x = -2.0 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2cos(1\u03c0x - 3) - 2) + 1, g(x) = -2|x + 1| + 2, x = -1.2, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((3x - 3)/(-1x + 3)) + 1)/(-3((3x - 3)/(-1x + 3)) - 1) and g(x) = 2|x - 1| - 1 from x = 0.4 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0((-1x + 3)/(-3x + 1)) - 3) - 2, g(x) = -3|x - 3| + 3, x = 0.7, and x = 0.7999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(2\u03c0(-3x^2 + 2x + 2) - 3) + 1, g(x) = (3x - 2)/(1x), x = 1.5, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(3sin(3\u03c0x + 2) + 1)^2 - 2(3sin(3\u03c0x + 2) + 1) and g(x) = -3|x - 2| - 2 from x = -0.2 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0((-3x - 3)/(3x + 3)) - 2) + 3 and g(x) = -1|x - 2| + 2 between the vertical lines x = 1.2 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1|x| - 3) + 1| and g(x) = (-1x + 2)/(3x + 1) between the vertical lines x = -2.2 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2cos(2\u03c0x + 1) + 1)^2 - 1(2cos(2\u03c0x + 1) + 1) - 3, g(x) = -1x - 5, x = -3.4, and x = -3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(4x^2 - 2x - 3) + 2| + 2, g(x) = -1|x - 1| + 3, x = -0.3, and x = -0.19999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3|x + 2| + 1) - 2)/(3(-3|x + 2| + 1) - 2) and g(x) = -4x^2 + 5 between the vertical lines x = -1.9 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(1\u03c0x - 2) + 2)^2 + 5(-1cos(1\u03c0x - 2) + 2) + 2, g(x) = -3x + 3, x = -3.8, and x = -3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2cos(3\u03c0x - 1) - 2) + 2)/(-3(2cos(3\u03c0x - 1) - 2) + 2) and g(x) = (3x + 3)/(1x - 3) between the vertical lines x = -2.6 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(5x^2 + 4x - 4) + 1| + 2 and g(x) = (-2x - 1)/(-1x - 2) between the vertical lines x = -0.9 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1x^2 - 3x + 1) + 1 and g(x) = 1|x| - 3 between the vertical lines x = 1.5 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2e^(1(-1|x - 1| + 1)) + 2, g(x) = 4x^2 + 1x - 3, x = -1.2, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(1sin(3\u03c0x + 3)) - 5 and g(x) = -3|x| - 3 between the vertical lines x = -0.4 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2cos(3\u03c0x - 1) - 3) + 3, g(x) = (-2x - 1)/(1x - 2), x = 4.7, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(3x^2 - 5x + 1) + 1)/(2(3x^2 - 5x + 1) + 1), g(x) = 1|x + 3|, x = 0.4, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0((3x - 1)/(3x + 1)) - 1) and g(x) = (1x + 1)/(-2x - 2) from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1|x - 3| - 2) - 1)/(2(1|x - 3| - 2) + 1) and g(x) = -2|x - 3| + 3 between the vertical lines x = 4.8 and x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(2\u03c0(5x^2 - 2x - 1) + 1) - 3, g(x) = (-1x + 2)/(-2x + 1), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-1x + 1) + 1| - 1 and g(x) = 4x^2 - 1x + 2 from x = -1.2 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(3\u03c0(-1x) - 2) - 3 and g(x) = (2x + 2)/(-2x - 2) from x = 2.4 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0((-1x)/(2x - 3)) - 1) + 1 and g(x) = 1x^2 - 4x + 3 from x = 1.2 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-2sin(3\u03c0x - 2) + 3) - 3| + 1, g(x) = 1x - 1, x = 0.3, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-1sin(3\u03c0x - 1)) + 3| - 3, g(x) = (-3x + 3)/(-2x + 3), x = 3.5, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1|x - 2| - 3)^2 - 3(1|x - 2| - 3) - 4 and g(x) = 2|x + 1| + 3 between the vertical lines x = 1.2 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-3cos(2\u03c0x) - 3) - 1 and g(x) = -5x + 5 between the vertical lines x = -1.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-3x + 3)/(2x - 1))^2 + 2((-3x + 3)/(2x - 1)) + 5 and g(x) = -3|x| between the vertical lines x = -3.3 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(1|x - 1| - 1)^2 - 5(1|x - 1| - 1) - 3 and g(x) = -3x + 1 from x = 1.0 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(3\u03c0(3|x| - 2) - 1) - 3 and g(x) = -5x^2 + 5x + 5 from x = -0.8 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2x - 5) + 2)/(-3(2x - 5) + 1) and g(x) = 4x + 2 between the vertical lines x = -0.6 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(2(-3|x| + 2)) - 1, g(x) = (-1x - 1)/(1x), x = -0.6, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3cos(3\u03c0x + 1) + 3) - 2| + 2 and g(x) = -2x^2 - 2x + 4 between the vertical lines x = -1.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3sin(1\u03c0x - 1) + 2) - 2)/(3(3sin(1\u03c0x - 1) + 2) - 2) and g(x) = -2x^2 + 3x - 5 from x = 0.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(2\u03c0(2|x - 1| - 3) - 1) + 1 and g(x) = -3x - 3 from x = -1.1 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0((-2x + 2)/(-1x - 1)) - 2) + 3, g(x) = 1|x - 3| + 3, x = 2.2, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2x - 5)^2 + 5(2x - 5) - 2 and g(x) = 1|x + 3| - 3 between the vertical lines x = 3.2 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(-1(-2x + 5)) + 3 and g(x) = 3|x + 3| - 2 between the vertical lines x = -1.3 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3x^2 + 3x - 3) - 5 and g(x) = 1|x - 1| from x = -1.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(-2x^2 + 4x + 2) - 2) + 2, g(x) = -4x - 1, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(1cos(3\u03c0x + 2) - 1) - 3 and g(x) = 1x - 3 from x = -4.7 to x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(4x - 1)| + 1 and g(x) = 1|x - 1| - 3 between the vertical lines x = -0.1 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-5x^2 - 5x + 5) + 3 and g(x) = (3x + 2)/(-1x + 2) from x = -1.2 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1sin(3\u03c0x + 3) - 3) - 2)/(1(1sin(3\u03c0x + 3) - 3) + 2), g(x) = 2x^2 + 5x + 2, x = 3.2, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3e^(-1x) - 3) + 1)/(1(-3e^(-1x) - 3) - 2), g(x) = 2|x - 1| - 3, x = 0.3, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2sin(1\u03c0x + 1) + 1) + 5, g(x) = 3x + 1, x = -0.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2x^2 - 4x - 1) + 3 and g(x) = (-1x - 2)/(-3x + 2) between the vertical lines x = -1.9 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2cos(2\u03c0x + 1) + 1) - 1, g(x) = 4x^2 + 1, x = 0.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(1(-1|x + 3| - 2)) + 3, g(x) = 3|x - 1| + 1, x = 0.3, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-2sin(1\u03c0x + 3) + 1)^2 + 3(-2sin(1\u03c0x + 3) + 1) - 2, g(x) = 5x - 5, x = 3.0, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(-1|x - 3|)), g(x) = (1x - 3)/(2x + 2), x = 0.6, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(4x - 3) + 3 and g(x) = (-2x + 1)/(-1x) from x = -0.1 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(-3x - 5)) + 3 and g(x) = 1|x + 1| - 1 between the vertical lines x = 2.9 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-5x + 1)^2 + 5 and g(x) = 1|x - 1| + 2 from x = 0.1 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((2x + 1)/(2x - 3))^2 + 4((2x + 1)/(2x - 3)) - 1 and g(x) = (2x - 2)/(3x - 2) from x = 0.7 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2x) + 1)/(1(2x)), g(x) = -2|x + 2| + 3, x = -2.6, and x = -1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(1x^2 + 3x - 2)^2 + 2(1x^2 + 3x - 2) - 1 and g(x) = 1x - 1 from x = -3.8 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(-1|x + 1|) + 2) and g(x) = -1|x + 3| + 3 from x = -0.6 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2sin(2\u03c0x + 1)) - 2, g(x) = 5x + 1, x = -0.7, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1|x - 1| + 3) + 1)/(3(-1|x - 1| + 3) + 2) and g(x) = -1|x - 2| + 2 from x = 3.2 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2x) + 2| - 3, g(x) = -2|x + 3| - 1, x = 0.2, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-2x - 4)^2 - 5(-2x - 4) + 2 and g(x) = 1x - 1 from x = -2.4 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3cos(1\u03c0x - 3) + 3)^2 + 1(3cos(1\u03c0x - 3) + 3) + 2 and g(x) = (2x - 3)/(-2x) between the vertical lines x = -3.7 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2cos(2\u03c0x - 1) - 2) - 5, g(x) = -1x^2 + 2x + 5, x = -3.6, and x = -3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0((-3x - 3)/(1x + 3)) + 2) + 1 and g(x) = -1x - 2 from x = -3.5 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(3e^(-2x) - 3) + 2)/(-2(3e^(-2x) - 3) + 3) and g(x) = -3x + 2 from x = -0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-1x^2 + 4x + 3) - 4 and g(x) = (1x + 3)/(-1x + 2) from x = 2.2 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1\u03c0(-5x^2 - 3x - 3) - 2) - 3 and g(x) = -2x^2 - 4x - 5 between the vertical lines x = 0.2 and x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3sin(1\u03c0x) + 3) - 3)/(-1(3sin(1\u03c0x) + 3) + 2) and g(x) = -1x + 4 between the vertical lines x = -0.9 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(5x^2 + 1x - 4)^2 - 3(5x^2 + 1x - 4) + 3 and g(x) = (1x - 1)/(2x - 1) from x = -0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-1cos(2\u03c0x))^2 - 5(-1cos(2\u03c0x)) - 1 and g(x) = 1|x + 2| - 1 from x = -3.2 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-3sin(3\u03c0x + 3) - 1)^2 + 3(-3sin(3\u03c0x + 3) - 1) + 3, g(x) = -4x^2 - 5x + 2, x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(3e^(1x) - 2) - 1| + 2, g(x) = (-3x + 2)/(3x + 1), x = 0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(3cos(2\u03c0x) + 3) - 2, g(x) = 5x + 5, x = -3.3, and x = -2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(3x^2 + 1x - 1)| + 1 and g(x) = -3x^2 - 3x + 2 from x = 0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2((1x + 1)/(2x + 1)) - 2)/(-3((1x + 1)/(2x + 1)) - 1) and g(x) = (-1x + 2)/(1x - 3) between the vertical lines x = -0.7 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(-1x + 2) - 2) + 2 and g(x) = -2x + 3 between the vertical lines x = 0.4 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(5x - 5) + 4 and g(x) = (-1x - 2)/(-3x - 1) between the vertical lines x = -0.5 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|x| + 1) + 3| - 1, g(x) = 3|x - 1| + 1, x = -0.4, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-1sin(1\u03c0x + 2)) - 2| + 1 and g(x) = 1x^2 - 2x + 4 from x = 1.4 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2x^2 + 3x - 3)^2 + 5(2x^2 + 3x - 3) - 3 and g(x) = (3x - 2)/(-1x + 2) from x = -2.5 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(1\u03c0(-2x^2 - 5x + 1) - 1), g(x) = 5x^2 - 2x - 2, x = -0.3, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1x^2 - 2x + 1)^2 - 5(1x^2 - 2x + 1) + 4 and g(x) = (2x - 1)/(-2x + 1) from x = -0.9 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-2x + 3) + 1, g(x) = 3x^2 + 1x + 3, x = -3.1, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1x^2 - 1x - 1))/(-1(1x^2 - 1x - 1) + 2), g(x) = 3x^2 - 3x + 2, x = -1.4, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(2\u03c0(1x + 1) - 3) - 2, g(x) = 1|x - 2| - 2, x = 1.4, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(5x^2 - 3x - 4)^2 - 4(5x^2 - 3x - 4) + 2 and g(x) = (-3x + 1)/(2x) from x = -0.4 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3|x + 2| - 1)^2 + 5(3|x + 2| - 1) - 3 and g(x) = -3x - 3 from x = -2.6 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((2x + 3)/(1x + 2))^2 - 4((2x + 3)/(1x + 2)) - 3 and g(x) = -5x^2 + 4x - 1 from x = -2.8 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0(1|x| + 1) - 1) + 1 and g(x) = -2|x - 1| + 1 between the vertical lines x = 1.1 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0(-2x + 4) - 1) - 1 and g(x) = -5x^2 + 5x - 2 from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0((-1x + 3)/(-1x + 2)) + 2) - 2 and g(x) = -2|x - 2| from x = 2.1 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((2x - 3)/(3x + 1)) + 4 and g(x) = (1x + 1)/(-3x - 2) from x = -0.8 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(3sin(1\u03c0x - 1)) + 3 and g(x) = (1x + 1)/(-1x + 2) from x = -3.8 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-1x)/(-3x)) + 1|, g(x) = -2x^2 + 3x - 1, x = -0.4, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2x - 4) + 3 and g(x) = (3x)/(1x - 2) from x = -1.6 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3sin(3\u03c0x + 3) + 1) + 3| - 1 and g(x) = -5x^2 - 4x + 3 between the vertical lines x = -0.2 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(5x^2 - 4x - 1) - 3, g(x) = -4x - 5, x = -0.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((-3x - 2)/(-3x)) + 3| - 3, g(x) = -5x^2 - 4x + 1, x = -0.4, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1cos(2\u03c0x + 3) - 1) + 1)/(-2(-1cos(2\u03c0x + 3) - 1) + 1) and g(x) = 1x^2 - 4x from x = -0.1 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1e^(1x) + 2) - 3)/(-3(-1e^(1x) + 2) - 2), g(x) = (1x + 3)/(2x + 3), x = -2.7, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((3x - 1)/(-3x - 1))^2 - 5((3x - 1)/(-3x - 1)) - 5 and g(x) = -4x^2 - 1x - 5 from x = -0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3e^(1x) - 2)^2 + 5(3e^(1x) - 2) - 3, g(x) = -5x - 4, x = -0.3, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2|x + 3| - 2) + 3)/(2(-2|x + 3| - 2) + 3) and g(x) = 1|x + 2| between the vertical lines x = -3.0 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|x - 1|)^2 + 4(-3|x - 1|) + 2 and g(x) = -3x^2 + 3x - 1 between the vertical lines x = 0.8 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2e^(-2(-2x + 2)) + 2 and g(x) = 1|x + 3| - 1 from x = 0.0 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(4x) + 3)/(-1(4x) - 1) and g(x) = (-3x + 2)/(1x + 2) between the vertical lines x = -0.4 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-3x - 2)/(1x - 3)) - 1, g(x) = 1|x + 1| - 1, x = -1.6, and x = -0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-4x^2 + 3x + 5) + 4 and g(x) = -1|x + 1| - 1 from x = -1.3 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(3\u03c0(-1x - 1)) - 1, g(x) = 5x, x = -0.4, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(2|x + 1| - 3) - 2), g(x) = 2x - 2, x = 1.3, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-3x^2 + 3x + 1) + 4 and g(x) = (1x - 3)/(-3x - 3) between the vertical lines x = -0.9 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2sin(2\u03c0x - 3) + 1) - 1)/(-1(2sin(2\u03c0x - 3) + 1) + 2) and g(x) = 1x^2 - 5x + 5 from x = -3.4 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-3cos(3\u03c0x + 2) - 1) - 4, g(x) = 2|x + 2| - 2, x = -2.6, and x = -2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(2(2x^2 + 1x - 4)) + 2, g(x) = 2x^2 + 3x + 2, x = 0.0, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(2|x + 2|)) + 1, g(x) = -2|x - 2| + 2, x = 0.9, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2\u03c0((1x + 3)/(3x + 2)) - 1) - 3 and g(x) = (-1x + 3)/(3x - 2) between the vertical lines x = -0.5 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(2\u03c0(-3|x + 1| - 2) - 2) + 2, g(x) = (1x - 2)/(-1x + 2), x = -4.4, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2((2x + 3)/(3x + 3)) - 3 and g(x) = (-2x + 2)/(-1x + 2) from x = -0.8 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(3\u03c0((1x - 3)/(1x)) + 1) - 2, g(x) = 5x^2 + 5x - 2, x = -0.2, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1cos(3\u03c0x + 3) + 3) - 3)/(2(-1cos(3\u03c0x + 3) + 3) - 3), g(x) = -3x^2 - 5x + 2, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(1sin(3\u03c0x - 1)) + 2)/(2(1sin(3\u03c0x - 1)) - 1), g(x) = (3x - 3)/(-1x - 2), x = -3.8, and x = -3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(1x - 2)^2 + 2(1x - 2) + 4, g(x) = (-3x)/(-2x - 2), x = 1.3, and x = 3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0(-1x - 3)) and g(x) = -1x^2 - 1x + 4 between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0(-5x + 2) - 3), g(x) = 2x^2 - 4x + 2, x = 1.0, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2e^(1(1x - 2)) - 2, g(x) = -3|x| + 2, x = 2.0, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(1(1x - 1)) - 1 and g(x) = (-3x - 1)/(-1x) between the vertical lines x = -0.3 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0(-1x - 4)) - 2 and g(x) = 3x^2 + 5x - 5 from x = -2.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((2x)/(-1x + 2)) - 3| - 1 and g(x) = -1x - 2 from x = 1.0 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(2\u03c0((-3x - 3)/(-1x + 2)) - 1) - 1 and g(x) = (-2x + 1)/(2x - 3) from x = 2.3 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1\u03c0(-1|x + 3|)) - 1 and g(x) = (-1x - 3)/(1x + 2) between the vertical lines x = -4.2 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(3\u03c0((-3x - 3)/(1x + 3))) - 2, g(x) = -1x^2 + 5x, x = -0.1, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(1x^2 - 5), g(x) = -1x + 2, x = -1.3, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(3|x| - 1) - 3| + 2 and g(x) = 2|x| - 2 between the vertical lines x = 1.0 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(2\u03c0(-1|x| + 3) - 3) + 1 and g(x) = -4x^2 - 5x + 1 from x = -0.1 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1((3x + 3)/(-1x + 3)) - 1)/(2((3x + 3)/(-1x + 3)) - 1) and g(x) = -5x - 3 from x = -0.8 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(5x^2 + 5x - 1)| + 2 and g(x) = -3|x + 3| + 3 from x = -1.6 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(1e^(1x) + 1) - 2| + 2 and g(x) = -4x^2 + 3 from x = -0.4 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(-1(-2|x + 1|)) - 1, g(x) = (-3x - 1)/(-1x), x = -0.8, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(5x) + 3 and g(x) = (3x - 2)/(-3x - 2) from x = -0.6 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-3cos(1\u03c0x + 3) - 2))/(-1(-3cos(1\u03c0x + 3) - 2) - 1), g(x) = -3x + 2, x = 1.7, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(2|x - 3| - 3) - 2)/(3(2|x - 3| - 3) + 2), g(x) = -2x - 1, x = -0.1, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(-2(2x^2 - 4x - 1)) - 1 and g(x) = -4x - 4 between the vertical lines x = -0.8 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3sin(1\u03c0x - 2) + 3)^2 + 4(-3sin(1\u03c0x - 2) + 3) and g(x) = -3x^2 + 3x + 4 between the vertical lines x = -1.7 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0(3x - 2) - 1) - 2 and g(x) = -4x^2 - 2x + 3 from x = -1.5 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0(-3x) + 1) - 2 and g(x) = -3|x - 3| - 1 from x = 2.3 to x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(-2(2x^2 - 1)) - 3 and g(x) = 2x^2 - 4x + 1 from x = -0.3 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3|x - 2|)^2 - 4(-3|x - 2|) + 1, g(x) = 1|x - 2| + 2, x = 1.9, and x = 2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2x + 1)^2 - 1(-2x + 1) + 4 and g(x) = 3|x - 3| + 3 from x = -0.8 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(2x^2 + 3x - 1) - 3|, g(x) = -4x^2 - 1x + 2, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(-5x - 4)) + 1 and g(x) = -3x - 1 between the vertical lines x = -0.4 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(3sin(2\u03c0x - 2) - 1)^2 + 2(3sin(2\u03c0x - 2) - 1) + 2, g(x) = 3x^2 + 3, x = 0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0((2x - 1)/(3x)) - 3) - 2 and g(x) = -3x^2 + 2x + 1 from x = -0.5 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-4x + 4) + 2 and g(x) = (-1x + 1)/(-3x) from x = -0.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2e^(1x) - 1))/(-1(-2e^(1x) - 1) - 3) and g(x) = -2x^2 - 2x + 5 between the vertical lines x = 0.4 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(1cos(3\u03c0x - 1) - 2) + 1| - 1 and g(x) = -2|x| + 2 between the vertical lines x = -1.3 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-3cos(2\u03c0x + 1)) - 2)/(1(-3cos(2\u03c0x + 1)) + 2) and g(x) = (2x + 3)/(1x - 3) from x = 0.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1e^(-1x) + 2)^2 + 3(-1e^(-1x) + 2) - 1 and g(x) = 5x^2 + 3x from x = -0.5 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(5x^2 + 3x + 4) + 3)/(-2(5x^2 + 3x + 4) + 1) and g(x) = 1x^2 - 3x - 2 between the vertical lines x = 0.0 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(1\u03c0(-1|x + 3| - 2) - 2) + 3, g(x) = (2x + 1)/(2x + 2), x = -4.5, and x = -4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(3\u03c0((1x + 2)/(3x + 1)) - 1) and g(x) = -2x + 4 from x = 0.6 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2\u03c0(-1|x| + 2) - 3) + 2 and g(x) = 3|x - 2| + 2 between the vertical lines x = 1.8 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-4x^2 - 2x - 1)^2 - 3(-4x^2 - 2x - 1) + 2, g(x) = 5x^2 + 1x - 5, x = -0.9, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1x^2 + 1) - 3)/(3(1x^2 + 1) - 2) and g(x) = 1|x + 3| - 1 between the vertical lines x = -5.0 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-5x^2 - 5x + 5) - 2)/(2(-5x^2 - 5x + 5)) and g(x) = -5x + 1 between the vertical lines x = -1.6 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2x - 3) - 2)/(2(2x - 3) + 1) and g(x) = 3|x + 1| - 2 from x = -1.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1sin(3\u03c0x)))/(3(-1sin(3\u03c0x)) - 2) and g(x) = -1x + 5 from x = -2.9 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(-5x - 1) + 1), g(x) = (-1x + 1)/(2x + 2), x = 3.4, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0(1x^2 + 5x - 2) + 2) and g(x) = (-3x - 3)/(1x - 3) from x = -4.8 to x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(1cos(3\u03c0x + 3) + 1) - 5 and g(x) = 3x + 4 from x = -3.9 to x = -3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(1cos(3\u03c0x + 2) - 3) + 3| + 2, g(x) = (-1x + 2)/(2x + 3), x = -0.7, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-1e^(-2x) + 2) + 1)/(1(-1e^(-2x) + 2)), g(x) = (1x - 2)/(-2x + 3), x = -0.2, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((-1x + 1)/(-3x + 4))^2 - 5((-1x + 1)/(-3x + 4)) - 4, g(x) = (-2x + 3)/(-2x + 3), x = 1.2, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1cos(3\u03c0x + 2)) + 2)/(1(-1cos(3\u03c0x + 2))) and g(x) = -2|x + 2| - 3 between the vertical lines x = 3.0 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-3x - 2)/(-2x - 3)) - 4 and g(x) = (2x - 2)/(3x - 2) from x = -1.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((2x)/(1x + 1)) + 5 and g(x) = (-2x + 2)/(-3x + 1) from x = -0.3 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2sin(1\u03c0x) - 1) + 1)/(-2(2sin(1\u03c0x) - 1) + 1) and g(x) = 4x^2 + 5x + 2 from x = -1.2 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-3x^2 - 2x - 3))/(-3(-3x^2 - 2x - 3) + 4), g(x) = 1|x + 2| - 2, x = -3.7, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3x^2 + 5x)^2 - 4(-3x^2 + 5x) - 2 and g(x) = 1x - 5 from x = -0.7 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3sin(1\u03c0x - 2) + 3)|, g(x) = -5x + 2, x = -1.2, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-1sin(2\u03c0x + 3) - 2)| + 3, g(x) = 2|x - 2| - 2, x = 3.1, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(3\u03c0(-3|x - 1| - 1) + 1) - 1 and g(x) = -4x + 3 between the vertical lines x = 1.1 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-5x^2 - 5x + 3) - 1 and g(x) = 3|x - 3| - 1 between the vertical lines x = -1.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2cos(3\u03c0x + 1) + 1) - 2| + 2 and g(x) = (-1x - 1)/(-1x + 2) between the vertical lines x = 4.8 and x = 4.8999999999999995. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(1e^(-1x) - 3) - 1| + 1 and g(x) = 1x^2 - 4x - 3 from x = -0.3 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0(1x - 3) - 3) - 1 and g(x) = 4x + 3 from x = -1.1 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-3sin(2\u03c0x - 1) - 2) + 3)/(2(-3sin(2\u03c0x - 1) - 2)), g(x) = -3|x - 1| - 1, x = -4.0, and x = -3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(4x - 1)| - 1, g(x) = 2x + 4, x = -0.7, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((2x)/(-2x + 3))^2 + 4((2x)/(-2x + 3)) + 5 and g(x) = 1x^2 - 2x + 1 between the vertical lines x = -0.8 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3|x - 2| + 1) - 3)/(-1(-3|x - 2| + 1) + 3) and g(x) = -2x^2 + 4x + 2 between the vertical lines x = -0.2 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(4x^2 - 5x + 2) - 3)/(-1(4x^2 - 5x + 2)) and g(x) = -2|x - 3| + 1 from x = 1.5 to x = 5.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-3|x + 3| + 1) - 1 and g(x) = (-2x - 1)/(3x - 2) from x = -3.4 to x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-5x^2 + 4x) - 5 and g(x) = (-1x)/(-3x - 1) from x = -0.4 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-1|x + 3| - 1) + 3 and g(x) = -4x^2 + 2x - 5 between the vertical lines x = 0.0 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(2|x + 2| - 3)^2 + 2(2|x + 2| - 3) - 1 and g(x) = 5x + 1 between the vertical lines x = -2.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-3cos(3\u03c0x - 2) + 2)^2 + 4(-3cos(3\u03c0x - 2) + 2) + 2 and g(x) = -5x + 5 from x = 1.5 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(3x - 4)^2 + 5(3x - 4) - 4 and g(x) = 3|x - 3| + 2 between the vertical lines x = 0.6 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(3cos(3\u03c0x - 1)) - 3| + 3, g(x) = -3|x| - 1, x = 2.4, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1sin(1\u03c0x + 1) + 2)^2 - 2(1sin(1\u03c0x + 1) + 2) + 5 and g(x) = 5x + 3 between the vertical lines x = -1.4 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2\u03c0(4x^2 - 5x - 2) - 3) - 2 and g(x) = (-2x - 1)/(-1x - 3) between the vertical lines x = -1.0 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2sin(3\u03c0x + 3) + 2) + 3)/(-1(-2sin(3\u03c0x + 3) + 2) - 2) and g(x) = (-1x - 1)/(3x - 2) between the vertical lines x = -1.7 and x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3sin(1\u03c0x + 2)) - 4 and g(x) = -5x^2 - 5x + 1 between the vertical lines x = -0.5 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-2x + 1)/(3x))^2 + 4((-2x + 1)/(3x)) + 5 and g(x) = 2x + 1 from x = 0.1 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(1\u03c0(1|x - 1| - 2) - 3) + 1 and g(x) = 4x - 2 between the vertical lines x = 0.0 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-1|x - 1| + 1) - 3 and g(x) = -1|x - 1| - 1 from x = -0.2 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2sin(2\u03c0x + 3) + 2) - 2, g(x) = (-2x + 3)/(-3x - 1), x = -4.4, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-1x + 3)/(-1x + 2)) + 3, g(x) = -4x - 4, x = -0.7, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2sin(2\u03c0x - 1) + 1)^2 + 5(2sin(2\u03c0x - 1) + 1) - 2 and g(x) = 4x^2 + 4x - 2 from x = 1.2 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2\u03c0(-5x + 5) + 3) - 2 and g(x) = -2|x - 2| - 3 between the vertical lines x = 2.6 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3sin(3\u03c0x + 3) + 1)| + 1 and g(x) = -3x between the vertical lines x = 0.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(3x) + 4 and g(x) = 2x^2 + 3x + 4 from x = -4.5 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-3sin(3\u03c0x - 2) - 1)^2 + 5(-3sin(3\u03c0x - 2) - 1), g(x) = -1x + 5, x = 2.6, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0((3x)/(-2x - 2)) - 2) and g(x) = 3x + 4 between the vertical lines x = -0.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-1x)^2 + 1(-1x) + 1 and g(x) = 2x + 2 from x = -1.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(2\u03c0(-1x - 3)) - 2 and g(x) = -3x + 3 from x = 1.8 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0((-2x + 3)/(-2x - 1)) + 1) + 1 and g(x) = 4x - 2 from x = 0.5 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(2x^2 - 4x + 1) + 1) - 1 and g(x) = (2x + 1)/(-3x + 2) from x = -4.5 to x = -4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(5x - 4) - 2| + 2 and g(x) = 2x + 1 from x = 1.1 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(2sin(1\u03c0x - 1) - 2) + 3| and g(x) = -3|x - 2| + 2 from x = 1.4 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-4x + 3) - 2)/(2(-4x + 3)), g(x) = 2x^2 - 1x - 3, x = -1.2, and x = 0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-2x + 2)/(-3x + 2)) + 2| and g(x) = (3x + 2)/(3x + 1) from x = -0.2 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-5x + 4)^2 - 5(-5x + 4) + 1, g(x) = -2|x + 1| - 2, x = 0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3\u03c0(-3|x + 1| + 3) + 2) - 3 and g(x) = -3|x - 3| + 3 between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(1sin(1\u03c0x + 3) - 1) - 1| + 2, g(x) = (1x - 2)/(1x), x = 3.2, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1\u03c0((-1x - 1)/(-2x - 3))) - 2 and g(x) = -2x - 4 between the vertical lines x = -1.4 and x = -1.2999999999999998. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((-3x - 2)/(1x + 3))^2 + 2((-3x - 2)/(1x + 3)) - 4 and g(x) = -1x^2 - 4x + 4 between the vertical lines x = -1.4 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(-1(-3|x + 2| - 1)) - 2, g(x) = -2x + 5, x = -2.5, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-1cos(1\u03c0x + 2) - 2)| - 2 and g(x) = -1|x + 1| + 1 between the vertical lines x = 4.2 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(-3cos(2\u03c0x)) + 2, g(x) = 2|x - 3| - 2, x = 4.3, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-4x - 1) + 3 and g(x) = 3x^2 - 3x - 1 from x = -4.3 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2\u03c0((3x + 1)/(2x + 2))) and g(x) = 1x + 2 between the vertical lines x = -1.2 and x = -1.0999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(-4x^2 + 1x + 4) + 3) and g(x) = (3x + 3)/(2x - 1) between the vertical lines x = -3.0 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(-1(-1x + 4)) + 1 and g(x) = -3|x + 3| + 3 between the vertical lines x = -3.7 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2e^(-1x) - 2)| - 3 and g(x) = -4x^2 + 1x + 3 between the vertical lines x = -0.5 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-5x^2 - 5x - 1)^2 + 5(-5x^2 - 5x - 1) + 4 and g(x) = -3|x + 2| + 1 from x = -0.9 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3sin(3\u03c0x - 1) + 3)^2 + 5 and g(x) = -2x^2 + 4x + 2 between the vertical lines x = -1.0 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2cos(3\u03c0x) - 1) - 2, g(x) = (3x + 1)/(1x + 3), x = 3.0, and x = 3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2\u03c0(-1x^2 + 5x + 3) - 2) and g(x) = (-1x - 2)/(-2x - 2) between the vertical lines x = 0.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(2sin(1\u03c0x - 2) - 1) - 2)/(2(2sin(1\u03c0x - 2) - 1) - 1) and g(x) = 5x - 4 between the vertical lines x = -2.6 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(1cos(3\u03c0x - 3) - 1) + 4 and g(x) = 1x + 1 from x = 4.2 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(2cos(1\u03c0x) - 1) - 5, g(x) = -3x^2 - 2x - 2, x = -1.5, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(3\u03c0(3|x - 2| - 1) - 2), g(x) = -1x - 3, x = -3.2, and x = -3.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2|x - 2|)^2 - 4(2|x - 2|) - 4, g(x) = -4x + 2, x = 1.8, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2|x - 2| - 3) + 1)/(-2(2|x - 2| - 3)), g(x) = (2x + 2)/(1x + 1), x = 0.6, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1\u03c0(-2|x - 3| + 1) - 3) + 1 and g(x) = (3x - 1)/(-3x - 3) between the vertical lines x = 0.9 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(3\u03c0(-3x^2 + 4x + 3) - 1) - 1 and g(x) = 4x^2 + 1x - 4 from x = 0.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-3sin(3\u03c0x - 3) + 2))/(-3(-3sin(3\u03c0x - 3) + 2) - 1), g(x) = (-1x - 1)/(3x - 1), x = -3.6, and x = -3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1\u03c0(5x^2 + 3x - 3) - 2) and g(x) = -5x + 5 between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(-3|x + 2| + 1) + 2) - 1 and g(x) = (3x + 3)/(-3x) between the vertical lines x = 2.5 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(1cos(3\u03c0x + 2) + 1) + 3| and g(x) = 1|x + 2| + 3 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2x + 5)^2 + 5(-2x + 5) + 4 and g(x) = 4x + 2 between the vertical lines x = 2.1 and x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0(-1x^2 + 3x)) and g(x) = -1x^2 + 5 between the vertical lines x = -2.3 and x = -2.1999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(1cos(2\u03c0x - 2) - 3) + 4, g(x) = -2|x + 1| + 2, x = 4.2, and x = 4.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-5x) - 1| and g(x) = -1x^2 - 4 from x = -0.5 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-3cos(1\u03c0x)) + 3| + 1, g(x) = (-2x)/(-3x - 2), x = -0.6, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-1|x + 1| - 1) - 1| + 3, g(x) = -3|x| + 2, x = -0.5, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-3cos(2\u03c0x + 3) + 2) - 4 and g(x) = -1|x + 3| - 2 from x = 1.3 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3x + 5))/(2(-3x + 5) - 1) and g(x) = 1x + 2 between the vertical lines x = -3.0 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(5x - 2) + 3) - 1 and g(x) = 1|x - 2| - 3 from x = 0.8 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2x^2 - 4x + 1) + 1)/(-2(2x^2 - 4x + 1) + 3) and g(x) = -2x^2 - 1x - 4 between the vertical lines x = -0.1 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-2e^(1x) + 2) + 3)/(-3(-2e^(1x) + 2) + 2), g(x) = -2x^2 + 4x + 5, x = -1.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3sin(2\u03c0x - 2) - 2) - 5 and g(x) = -4x^2 - 5x + 1 between the vertical lines x = -2.2 and x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2x^2 + 1)^2 - 5(-2x^2 + 1) + 3 and g(x) = (2x - 3)/(-1x - 3) from x = -0.6 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(1x - 2)^2 - 3(1x - 2) - 5, g(x) = -3|x - 2| + 2, x = -2.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-1x^2 + 4x - 4) + 1| and g(x) = 1x - 4 between the vertical lines x = -0.3 and x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-3sin(1\u03c0x + 1) + 1) + 1| + 2, g(x) = -2x^2 + 3x - 3, x = 0.9, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(3cos(3\u03c0x - 1) - 1)^2 + 5(3cos(3\u03c0x - 1) - 1) - 4 and g(x) = (-3x)/(-2x - 2) from x = 1.5 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(4x - 5) - 2) + 2 and g(x) = -2|x + 2| from x = -1.8 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4x - 1) - 3 and g(x) = -3x^2 + 4x - 2 between the vertical lines x = 0.1 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1\u03c0((2x - 2)/(-1x - 2)) + 2) - 2 and g(x) = 3x^2 - 4x - 5 between the vertical lines x = -0.7 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(4x^2 + 5x + 1) + 2, g(x) = (2x + 2)/(1x - 2), x = 0.0, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(1\u03c0(-3x^2 + 1x + 5) - 3) - 2, g(x) = -1|x| + 2, x = 3.1, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3cos(1\u03c0x - 1) - 1) - 2)/(-3(3cos(1\u03c0x - 1) - 1) + 1), g(x) = 5x^2 + 3x - 4, x = -4.0, and x = -3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-3e^(2x) + 3)^2 - 3(-3e^(2x) + 3) - 5, g(x) = -3|x + 2|, x = -3.7, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(1\u03c0((-1x - 1)/(-3x + 1)) - 1) - 3 and g(x) = 4x - 3 from x = 0.1 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(5x + 1) - 2| + 2 and g(x) = (1x + 3)/(-1x - 1) from x = -0.6 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-1x - 4) - 3, g(x) = (-1x - 2)/(2x + 2), x = -3.5, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0((-1x + 1)/(-1x - 3)) - 1) + 3 and g(x) = -1x + 2 between the vertical lines x = -3.3 and x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2x^2 - 2x - 5) - 2)/(-3(-2x^2 - 2x - 5) + 2), g(x) = -2|x - 2|, x = 1.7, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(1\u03c0(-3x - 5) + 1) + 3 and g(x) = 3x^2 - 3x - 5 from x = -1.1 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(4x^2 + 3x - 1) + 1 and g(x) = (-1x - 3)/(1x) between the vertical lines x = -0.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(-2|x| - 2) + 1) + 1 and g(x) = 3|x - 2| from x = 1.8 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((1x - 2)/(2x - 3)) - 1, g(x) = (1x + 1)/(-3x + 1), x = 0.5, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(2\u03c0(-1x^2 - 5x)) + 1 and g(x) = 1x^2 - 3 from x = 1.1 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(1\u03c0((3x + 3)/(-1x + 2))) - 3, g(x) = -1x - 1, x = 1.6, and x = 1.7000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3sin(2\u03c0x + 3) - 1)^2 + 1(-3sin(2\u03c0x + 3) - 1) + 4 and g(x) = 2x between the vertical lines x = 3.9 and x = 4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-4x^2 + 5x + 1) + 2 and g(x) = 2|x + 3| + 1 between the vertical lines x = 0.2 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2cos(2\u03c0x - 1) - 3)^2 + 4(-2cos(2\u03c0x - 1) - 3) + 2, g(x) = 2x^2 - 4x - 1, x = 1.8, and x = 1.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0(-1x + 1) + 3) + 2 and g(x) = 3|x| + 1 between the vertical lines x = -1.2 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-5x - 4) + 3)/(-1(-5x - 4) - 2) and g(x) = 1x + 2 between the vertical lines x = -3.1 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3cos(1\u03c0x) - 2) and g(x) = 5x + 1 between the vertical lines x = -1.7 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(1\u03c0((2x)/(2x + 1)) - 2) + 2, g(x) = (-1x + 1)/(-1x - 1), x = -1.6, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-3cos(2\u03c0x - 1) + 1)^2 + 2(-3cos(2\u03c0x - 1) + 1) + 5 and g(x) = 2|x + 1| - 1 from x = 0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(1\u03c0(2|x| + 1) + 2) - 1, g(x) = (-2x - 2)/(3x), x = 2.4, and x = 3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|x - 3| + 3) - 3)/(-2(-1|x - 3| + 3) - 3) and g(x) = -3x^2 + 3 from x = -0.7 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3e^(-1x) - 1) - 3)/(-3(3e^(-1x) - 1) - 3), g(x) = -5x^2 + 5x + 4, x = -0.4, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(2\u03c0(3x^2 - 2x + 1) + 2) - 3, g(x) = (-3x - 2)/(2x - 3), x = -4.0, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1sin(2\u03c0x + 1) + 1)^2 - 5(-1sin(2\u03c0x + 1) + 1) - 3 and g(x) = -3|x + 2| + 1 between the vertical lines x = -3.8 and x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2|x - 2| + 3) + 1|, g(x) = 4x^2 + 4x - 1, x = -2.1, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(1\u03c0x) - 2) - 1)/(1(-3cos(1\u03c0x) - 2)) and g(x) = (1x - 3)/(-1x - 3) between the vertical lines x = 3.0 and x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0(1x - 2) - 2) + 2, g(x) = 3x^2 - 5x - 5, x = -0.7, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-3sin(2\u03c0x - 1) + 2) + 1, g(x) = -3x^2 - 3x + 4, x = -0.4, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(1x - 2) - 1 and g(x) = (2x - 3)/(-1x + 2) between the vertical lines x = 1.6 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1|x + 1| - 3) + 2)/(2(1|x + 1| - 3) - 1) and g(x) = -2|x| - 2 between the vertical lines x = -4.5 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-2|x + 2| + 2) + 2)/(-1(-2|x + 2| + 2)) and g(x) = -3x^2 - 2x from x = -0.7 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-4x - 3) - 2| + 1, g(x) = 2|x + 1| + 3, x = -2.5, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(1\u03c0(2x - 4) + 1) + 2, g(x) = -2x + 3, x = 1.0, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(-1x) - 1) + 1 and g(x) = 5x + 2 from x = -0.6 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(3|x + 1| - 1)^2 - 4(3|x + 1| - 1) - 1 and g(x) = (-2x)/(3x - 2) from x = -2.7 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2x + 4)^2 - 2 and g(x) = -2|x| + 2 from x = 1.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2x^2 - 5x - 2) + 3)/(1(2x^2 - 5x - 2) - 3) and g(x) = 2x^2 - 1x - 5 from x = -1.2 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3cos(1\u03c0x + 1))^2 + 2(-3cos(1\u03c0x + 1)) and g(x) = (2x)/(-2x + 1) from x = -4.7 to x = -4.6000000000000005. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(2x + 3) - 3) - 1 and g(x) = (-1x + 1)/(-3x + 4) between the vertical lines x = -0.4 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-5x^2 - 4x + 4) - 1| + 2 and g(x) = -2x + 3 between the vertical lines x = -1.5 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|x + 3| - 1) + 2 and g(x) = -2x^2 + 3x - 1 between the vertical lines x = -0.9 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-1cos(2\u03c0x + 2) - 3)| - 1 and g(x) = 1x + 1 from x = 0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(1\u03c0((2x - 3)/(2x - 1)) + 3) + 3, g(x) = -4x^2 - 3x + 1, x = -0.0, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2|x - 2| - 2)^2 + 3(-2|x - 2| - 2) - 2, g(x) = 1|x + 3| + 2, x = 0.7, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1\u03c0(1x^2 + 4x + 3) - 1) - 2 and g(x) = -2x^2 - 2x + 4 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3sin(1\u03c0x) - 2) + 1)/(1(-3sin(1\u03c0x) - 2)) and g(x) = -2|x - 3| - 1 from x = -0.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-2x)/(-3x + 4)) - 1| + 2 and g(x) = -1x^2 + 1x + 4 between the vertical lines x = -0.7 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0((1x + 1)/(3x)) + 2) - 3 and g(x) = -3|x| + 3 between the vertical lines x = -2.4 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(1cos(1\u03c0x - 3)) + 4, g(x) = -1x^2 + 1, x = 0.8, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(3|x - 2| - 2) - 1, g(x) = 3x + 3, x = 0.7, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2((2x + 1)/(1x - 3)) - 2)/(3((2x + 1)/(1x - 3)) + 1), g(x) = -1|x - 2| + 1, x = -0.7, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-3x - 2)/(2x)) - 3| and g(x) = -5x + 2 from x = -1.0 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-1x - 4) - 1)/(3(-1x - 4) + 1) and g(x) = 2x^2 - 5x + 1 from x = 0.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-5x^2 + 4) - 3| + 2 and g(x) = 3|x + 3| + 1 between the vertical lines x = -0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(1x^2 + 4x + 4) - 1| - 1, g(x) = 2|x - 2| - 2, x = -4.2, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-3|x + 2| + 3) - 1)/(-1(-3|x + 2| + 3) + 2) and g(x) = -5x + 4 from x = -1.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((3x + 2)/(3x + 3))^2 - 5((3x + 2)/(3x + 3)) - 4 and g(x) = 4x + 5 from x = -1.5 to x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(2\u03c0x - 3)) - 1)/(-1(-3cos(2\u03c0x - 3))) and g(x) = (1x - 3)/(-1x + 2) from x = 3.2 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2\u03c0(-1|x - 3| + 3) + 3) and g(x) = -2x^2 + 5x - 3 between the vertical lines x = 0.5 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(5x - 5) + 1) + 3 and g(x) = 4x^2 - 5 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-1sin(1\u03c0x + 2) + 3) - 3| - 1, g(x) = 4x^2 - 2x, x = -0.4, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1|x + 3| - 2)^2 + 4 and g(x) = 5x^2 + 1x - 4 from x = -1.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(3\u03c0(1x^2 - 2x + 1) - 3) + 2, g(x) = 1x^2 + 5x - 4, x = 0.6, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-3sin(1\u03c0x - 3)) - 3| + 1 and g(x) = (2x - 3)/(-2x + 3) from x = -3.9 to x = -3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-4x^2 - 3x + 3)) and g(x) = -1x^2 + 1x + 3 between the vertical lines x = 0.6 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3sin(1\u03c0x - 1) - 2) + 1)/(2(3sin(1\u03c0x - 1) - 2) + 1) and g(x) = 3|x| - 1 between the vertical lines x = -3.5 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(1(3x^2 - 2x - 5)) + 1 and g(x) = -3x - 5 between the vertical lines x = -1.0 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(5x^2 + 4x - 2) and g(x) = 3x + 5 from x = -1.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4 and g(x) = -4x^2 - 1x + 1 from x = 0.6 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3((1x)/(2x - 1)) - 1)/(-1((1x)/(2x - 1)) + 2) and g(x) = 1x^2 - 5x + 3 from x = 1.6 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(1((2x - 3)/(3x))) + 3 and g(x) = (2x - 3)/(1x - 2) between the vertical lines x = 0.9 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(3sin(3\u03c0x - 2) - 1), g(x) = 1x^2 - 2x + 3, x = 0.2, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0(1|x| + 3) - 1) - 1 and g(x) = -2x^2 + 5x - 2 from x = -0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(2x - 2)^2 - 1(2x - 2) + 5 and g(x) = 1|x| - 3 from x = 0.2 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0((-2x + 3)/(-1x - 3)) + 1) + 3, g(x) = 3x + 4, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1|x| + 2) - 3)/(-2(-1|x| + 2)), g(x) = -5x - 3, x = -1.6, and x = -1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(3\u03c0(-3|x|) + 3) + 1 and g(x) = -2|x - 2| + 3 from x = 2.9 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(3\u03c0(1x^2 - 1x + 5) - 1) + 1, g(x) = 4x + 5, x = -1.1, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1\u03c0(3x + 2) - 3) + 1 and g(x) = 1|x + 2| - 3 between the vertical lines x = 1.7 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2\u03c0(-2x - 1) + 1) + 2 and g(x) = 1x^2 - 1x + 3 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(2\u03c0(-4x^2 - 2x - 1) + 1) - 3 and g(x) = (3x + 1)/(1x + 2) from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(3sin(1\u03c0x - 1) - 3) - 2)/(1(3sin(1\u03c0x - 1) - 3) + 3), g(x) = (2x - 1)/(-1x + 2), x = 0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-2cos(3\u03c0x - 3) - 2) - 1| - 2 and g(x) = 4x^2 - 1x from x = -0.5 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(4x - 1)^2 + 5(4x - 1) - 1 and g(x) = -2|x - 2| + 2 from x = 0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(1(3|x - 2|)), g(x) = 2x^2 + 5x + 3, x = 1.2, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1|x - 2| - 2) - 3 and g(x) = 1x - 4 from x = -0.5 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3\u03c0((3x + 1)/(-1x + 3)) + 1) + 2 and g(x) = (-1x + 3)/(2x + 3) between the vertical lines x = 1.9 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((1x - 1)/(-3x - 1)) + 4, g(x) = 4x^2 + 2x - 4, x = -1.6, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2e^(-2(-3x^2 + 4)) + 3 and g(x) = -5x^2 - 2x + 5 from x = -0.9 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(2x + 4) + 1), g(x) = -1x^2 + 5x, x = -0.1, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1x^2 + 5x - 4) - 1)/(-1(1x^2 + 5x - 4) - 2) and g(x) = 3x - 3 from x = 0.5 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1x + 2) - 1, g(x) = (1x - 1)/(2x - 1), x = -2.8, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(3cos(2\u03c0x + 1)) - 5 and g(x) = 3x^2 - 3x - 1 between the vertical lines x = 0.6 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0((2x + 2)/(-2x)) + 3) and g(x) = 3|x + 3| from x = -3.2 to x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1cos(3\u03c0x + 2) + 3) - 1| - 3 and g(x) = 2x + 5 between the vertical lines x = -1.3 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-5x^2 + 2x + 5) + 1 and g(x) = -5x^2 - 1x + 1 between the vertical lines x = -0.9 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(1\u03c0x + 1) + 2) + 1, g(x) = 5x^2 - 1x - 5, x = -1.2, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1\u03c0(3x^2 - 4x - 3) + 2) and g(x) = -1|x + 1| between the vertical lines x = -2.2 and x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((-3x - 1)/(-1x - 3)) + 1)/(2((-3x - 1)/(-1x - 3)) + 2) and g(x) = -2|x + 1| + 2 from x = -0.6 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-1((-1x + 1)/(-1x + 3))) - 1 and g(x) = 4x + 1 between the vertical lines x = -0.3 and x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2sin(1\u03c0x - 3) + 1)^2 - 3(-2sin(1\u03c0x - 3) + 1) - 3, g(x) = 3x + 1, x = -3.1, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((-1x + 3)/(-1x + 2))^2 + 5((-1x + 3)/(-1x + 2)) + 5, g(x) = 3x^2 + 3x + 3, x = -1.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(5x - 3) - 3)/(2(5x - 3)) and g(x) = -2x + 5 between the vertical lines x = 0.5 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2\u03c0(1|x - 1| + 2) + 1) - 2 and g(x) = (1x + 2)/(-2x - 1) between the vertical lines x = -4.7 and x = -4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-3x^2 + 2x) - 3, g(x) = -2x^2 - 3, x = 0.0, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1sin(3\u03c0x + 1)) - 3 and g(x) = 3x + 5 between the vertical lines x = -3.0 and x = -2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(2cos(3\u03c0x - 3) + 2) - 1| + 2 and g(x) = 2x + 2 from x = 0.1 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(2|x + 2| - 1) + 2| - 2 and g(x) = (-2x - 1)/(-3x - 1) from x = -2.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(3x - 1) - 1) + 1 and g(x) = -1x - 1 between the vertical lines x = -2.9 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(2x^2 + 5x - 1) - 3 and g(x) = 1|x + 1| + 3 from x = -2.2 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-3|x - 1| + 3) - 1)/(3(-3|x - 1| + 3) + 2), g(x) = -2|x| - 3, x = -0.3, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(2cos(3\u03c0x + 1) - 1) + 2 and g(x) = -3x + 2 from x = -1.5 to x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(-2x - 2) - 1) - 1, g(x) = -4x^2 + 5x - 1, x = 1.1, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(-2|x - 3|) + 3) - 2, g(x) = (-1x + 1)/(2x + 3), x = -0.4, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((3x + 3)/(-1x - 1)) - 1)/(-1((3x + 3)/(-1x - 1)) + 2) and g(x) = 1x^2 - 1x + 1 from x = 0.0 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(1\u03c0(1x)) + 3, g(x) = -3|x - 3| + 2, x = 2.8, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4x^2 - 4x - 2) - 1)/(2(-4x^2 - 4x - 2)) and g(x) = -3|x - 3| + 2 between the vertical lines x = 2.0 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(1\u03c0(1x + 2) - 2) - 1 and g(x) = -2x + 2 from x = 1.7 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(5x^2 - 4x - 4) - 4 and g(x) = 1|x + 2| + 3 between the vertical lines x = -0.8 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-4x^2 + 5x + 1) + 2, g(x) = 2|x + 2| + 2, x = -0.5, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-3x - 1) + 2| + 1 and g(x) = 1|x| + 2 between the vertical lines x = 0.2 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-3sin(2\u03c0x + 3) - 1)^2 + 5(-3sin(2\u03c0x + 3) - 1) - 2, g(x) = -1x^2 - 3x + 1, x = 1.1, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(2\u03c0(-3x + 2) - 3) and g(x) = 1x^2 - 5x + 2 from x = 4.6 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(2cos(2\u03c0x) - 2) + 3| + 3, g(x) = 1|x - 1| - 3, x = 0.1, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-2cos(2\u03c0x - 1) - 1) + 1 and g(x) = (-2x + 2)/(-3x + 2) from x = 1.8 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-3cos(1\u03c0x + 3) - 2) - 1| - 3, g(x) = 3x^2 - 3x - 3, x = 0.0, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(1\u03c0x) - 3)^2 + 2(-2sin(1\u03c0x) - 3) + 2 and g(x) = 3x + 2 between the vertical lines x = -4.8 and x = -4.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(1cos(1\u03c0x - 1) + 2) + 1| + 1, g(x) = 2|x - 2| + 3, x = 1.7, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0(-1x^2 - 3x + 5) + 2) and g(x) = 3|x + 2| - 1 from x = -2.2 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3e^(-2(-4x^2 - 2x + 2)) - 3 and g(x) = -3x^2 - 1 from x = -0.8 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-1(1x + 3)) + 3 and g(x) = (3x - 3)/(-2x + 3) between the vertical lines x = -3.8 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(1x^2 + 3x + 1)^2 + 2(1x^2 + 3x + 1) and g(x) = -1x^2 - 5x - 4 between the vertical lines x = -2.9 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(2|x - 1| + 1) - 3)/(3(2|x - 1| + 1)), g(x) = -2|x| + 3, x = -2.1, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2|x|) - 2)/(-2(2|x|) + 3) and g(x) = -3|x + 2| - 1 from x = -0.7 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-2x + 2)/(-3x + 4))^2 - 1((-2x + 2)/(-3x + 4)) - 1, g(x) = 1x^2 + 5x - 1, x = -4.8, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((1x + 1)/(3x + 2))^2 - 5((1x + 1)/(3x + 2)) + 4 and g(x) = 1|x - 3| + 3 between the vertical lines x = -0.8 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(2\u03c0((-1x + 1)/(2x + 2)) + 3) and g(x) = (-1x + 2)/(3x) from x = -1.1 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2cos(1\u03c0x - 2) + 1) - 3)/(2(2cos(1\u03c0x - 2) + 1) - 1) and g(x) = -1|x| + 3 between the vertical lines x = -2.5 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1x) - 1)/(-2(1x) - 1) and g(x) = 5x^2 - 1x - 3 between the vertical lines x = -0.8 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3cos(3\u03c0x - 3) + 2) and g(x) = 5x^2 - 3x + 1 from x = -0.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1x + 4) - 3)/(-2(1x + 4) - 3), g(x) = (2x + 1)/(2x), x = -3.9, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(2\u03c0(-2x^2 + 3x - 3) - 3), g(x) = 3|x - 2| - 2, x = 2.2, and x = 2.3000000000000003. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(1sin(2\u03c0x - 3) + 3) - 1| - 2 and g(x) = 5x^2 + 3x - 2 from x = -1.5 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2cos(1\u03c0x - 2) - 3)| + 1, g(x) = -1|x| + 3, x = 0.4, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3|x - 1| + 2) - 1)/(3(3|x - 1| + 2) - 2), g(x) = 2|x - 3| - 1, x = 2.3, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2x^2 - 2x) - 2| - 3, g(x) = 2x^2 - 4x + 3, x = -4.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2|x + 2| + 2))/(-2(-2|x + 2| + 2) + 1) and g(x) = -1|x + 3| + 3 between the vertical lines x = -2.8 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-3cos(2\u03c0x + 2) - 2) + 1)/(-2(-3cos(2\u03c0x + 2) - 2) - 3) and g(x) = -2|x - 1| - 2 from x = 1.0 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-3x + 2)/(1x - 3)) - 2)/(-1((-3x + 2)/(1x - 3)) - 2), g(x) = 3|x| - 2, x = -1.0, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(2x^2 + 5x + 4) - 3| + 1 and g(x) = 5x^2 + 5x between the vertical lines x = -0.4 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2cos(2\u03c0x + 3) - 2)^2 + 5(-2cos(2\u03c0x + 3) - 2) + 1 and g(x) = 1x + 1 from x = -4.1 to x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(-1x + 4) + 1) - 2 and g(x) = (2x - 3)/(1x - 3) from x = 1.8 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2\u03c0(2x^2 - 3x - 2) - 3) + 2 and g(x) = 2x - 2 between the vertical lines x = 2.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-2sin(3\u03c0x - 3) - 1) - 2 and g(x) = -3x^2 + 1x - 2 from x = 0.0 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2\u03c0(4x^2 - 2x + 4)) + 2 and g(x) = (-2x + 2)/(2x - 1) between the vertical lines x = 1.0 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(2\u03c0(-4x - 3) - 3) - 2 and g(x) = -3x - 1 between the vertical lines x = 0.7 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2sin(1\u03c0x + 1) - 3)^2 + 2(-2sin(1\u03c0x + 1) - 3) - 4, g(x) = -2x - 5, x = -1.0, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3sin(3\u03c0x - 3) - 2) + 3)/(-1(-3sin(3\u03c0x - 3) - 2) - 2) and g(x) = 2x^2 - 2x + 5 from x = -4.3 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(2\u03c0(3|x + 2| + 1) + 1) - 2 and g(x) = 1|x + 1| - 3 between the vertical lines x = -2.6 and x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(1|x + 3| + 3) + 3) + 2 and g(x) = 1|x - 1| - 3 between the vertical lines x = -4.5 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-2x - 3)/(2x + 2)) - 3| - 2, g(x) = -3x + 5, x = -0.9, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2|x - 2|)| - 1, g(x) = 1x^2 - 3x + 3, x = -2.6, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-2x^2 + 1x - 3) + 1)/(2(-2x^2 + 1x - 3)), g(x) = 4x^2 + 1x - 5, x = -1.1, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0((2x)/(1x + 3)) - 2) and g(x) = (-1x + 3)/(2x - 1) from x = -2.8 to x = -2.6999999999999997. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-2x^2 - 3x - 2) + 3)/(-3(-2x^2 - 3x - 2) - 1) and g(x) = 1|x - 3| from x = 2.6 to x = 3.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-3cos(3\u03c0x - 2) - 2))/(-3(-3cos(3\u03c0x - 2) - 2) + 1) and g(x) = -2|x - 1| + 1 from x = 2.0 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1cos(1\u03c0x - 1) - 3) - 3 and g(x) = 2|x| - 2 between the vertical lines x = -4.2 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(3|x + 3| + 3) + 2) - 3 and g(x) = 4x^2 - 4x - 3 between the vertical lines x = 0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1\u03c0(-4x - 5) - 3) + 2 and g(x) = 1x between the vertical lines x = 2.6 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(3\u03c0(-2x^2 - 1x - 3) - 2) + 2, g(x) = 2|x - 3| - 3, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(2x) + 1) + 3, g(x) = -4x + 5, x = 0.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2cos(3\u03c0x + 1) + 2) + 1)/(-1(2cos(3\u03c0x + 1) + 2) + 2) and g(x) = 2x from x = 0.2 to x = 0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-3x + 3)/(-2x + 3))^2 + 5((-3x + 3)/(-2x + 3)) - 3, g(x) = -1x^2 + 1x + 5, x = -0.6, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0(-3|x|) - 1) - 2, g(x) = (2x - 2)/(-1x + 3), x = -2.1, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(2cos(1\u03c0x) + 2) and g(x) = -3|x + 1| + 2 between the vertical lines x = 0.7 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-2x^2 - 3x) + 4, g(x) = 2|x - 1| + 1, x = -1.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5x) - 3)/(-1(-5x) + 2), g(x) = (-3x + 1)/(2x + 1), x = -0.4, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(2cos(1\u03c0x - 1) - 1) + 2| - 1, g(x) = -5x + 5, x = 2.0, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-3x + 2)| + 1, g(x) = 4x + 2, x = 0.3, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(1\u03c0(-4x - 3) + 1) - 2, g(x) = -4x^2, x = -0.4, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-2sin(1\u03c0x + 3) + 3) - 2, g(x) = -3|x - 2| + 2, x = -0.1, and x = 4.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3x - 1) + 2)/(2(3x - 1) + 2), g(x) = (1x - 3)/(-3x - 2), x = -1.9, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3e^(-1x) + 1) + 1 and g(x) = (-2x + 1)/(-3x + 2) from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5x + 2) + 2)/(2(-5x + 2) + 1), g(x) = -2x - 3, x = -1.8, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1cos(1\u03c0x - 3) - 1) + 5 and g(x) = 1|x + 3| - 1 between the vertical lines x = 3.7 and x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0((-3x - 1)/(-2x - 1)) + 2) + 2 and g(x) = (-1x - 3)/(-3x - 3) from x = -0.5 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-3|x|)^2 + 1(-3|x|) - 3 and g(x) = (1x - 3)/(2x - 3) between the vertical lines x = 0.6 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-1e^(1x) - 1) + 1| - 2 and g(x) = (2x + 1)/(1x) between the vertical lines x = -0.5 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(4x))/(2(4x) + 3), g(x) = -2|x - 2| + 2, x = 1.4, and x = 2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3x^2 + 5x - 4) - 5 and g(x) = (-3x - 1)/(-3x - 2) between the vertical lines x = -1.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2sin(2\u03c0x - 1) + 2) - 5 and g(x) = (-1x)/(-1x - 2) from x = -1.2 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(2|x + 1| - 2)^2 + 2(2|x + 1| - 2) - 5 and g(x) = -1x + 3 from x = -0.9 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3e^(-2x) + 2) - 1| + 3 and g(x) = (1x)/(-3x + 1) from x = 0.1 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-1cos(3\u03c0x) - 3) - 1| + 2 and g(x) = 5x + 3 from x = 1.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-1x^2 + 1x + 3)| - 3 and g(x) = -4x^2 - 1x + 5 from x = -1.4 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-2x - 3)/(-3x - 2)) + 1)/(-2((-2x - 3)/(-3x - 2)) + 3) and g(x) = 2x + 5 between the vertical lines x = -2.5 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((-3x + 3)/(2x - 1))| - 3 and g(x) = (-2x - 2)/(-2x - 1) between the vertical lines x = -0.8 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3((-1x - 3)/(1x + 3)) - 3)/(1((-1x - 3)/(1x + 3)) + 2), g(x) = 4x^2 + 3x - 5, x = -1.6, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1x^2 - 1x + 2) + 3)/(-1(1x^2 - 1x + 2) - 1) and g(x) = -1x^2 + 2x + 3 from x = -1.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-3cos(3\u03c0x) - 1) - 1| + 1 and g(x) = -1x + 5 from x = 1.8 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-1x - 1) + 1, g(x) = (3x + 1)/(3x - 2), x = -0.8, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-2x + 2) + 1)/(-2(-2x + 2) - 3), g(x) = (2x - 2)/(-2x + 1), x = 1.2, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-2x^2 + 1x + 2) - 1)/(1(-2x^2 + 1x + 2)) and g(x) = -3x^2 - 1x + 4 from x = 0.8 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-3sin(3\u03c0x + 1) - 1) - 3| - 3, g(x) = -2x^2 - 5x + 5, x = 1.9, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1sin(3\u03c0x - 1) - 1)^2 - 2(1sin(3\u03c0x - 1) - 1) - 2 and g(x) = (1x + 1)/(1x + 3) between the vertical lines x = -1.2 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(3x + 4) - 2)/(-3(3x + 4) + 1) and g(x) = (3x)/(-3x - 3) from x = -1.3 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((2x - 3)/(2x + 1)) + 2)/(2((2x - 3)/(2x + 1)) - 3) and g(x) = -5x^2 + 1x + 4 from x = -0.9 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(-2(-5x + 1)) + 3 and g(x) = -4x - 3 between the vertical lines x = -1.5 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3sin(1\u03c0x + 3) - 1) + 3)/(-3(3sin(1\u03c0x + 3) - 1) + 1) and g(x) = 1x^2 - 3x - 3 from x = -4.8 to x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(-4x + 1) - 1) and g(x) = (2x + 3)/(2x + 1) between the vertical lines x = 3.7 and x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2((3x - 1)/(1x)) + 1)/(3((3x - 1)/(1x))) and g(x) = (3x - 3)/(-2x - 3) from x = 0.4 to x = 2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2e^(1x) - 3) - 2 and g(x) = -2|x| + 3 from x = -4.0 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-5x^2 + 2)^2 + 5(-5x^2 + 2) + 1 and g(x) = 4x - 1 between the vertical lines x = -0.8 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2cos(3\u03c0x + 3) + 1)^2 + 3(-2cos(3\u03c0x + 3) + 1) - 4 and g(x) = (3x)/(-1x + 2) between the vertical lines x = -0.2 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-2x - 2)/(-1x))^2 + 1((-2x - 2)/(-1x)) + 3, g(x) = -2x - 5, x = -2.5, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(3cos(1\u03c0x - 2)) + 2)/(-2(3cos(1\u03c0x - 2)) - 3) and g(x) = 3|x + 1| + 1 from x = -0.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(1sin(2\u03c0x + 1) - 1) + 3| + 1, g(x) = 3|x - 3| - 1, x = 0.9, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-3x - 2)/(-2x + 1)) - 3| - 1, g(x) = (2x + 3)/(-1x), x = 1.0, and x = 3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(1\u03c0(-3|x - 3| + 2) + 1), g(x) = -4x + 5, x = 0.8, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(2\u03c0(-3|x + 2| - 1) + 2) + 2, g(x) = 2|x - 1| - 3, x = -2.5, and x = -2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(1cos(3\u03c0x - 3) + 3) + 1| - 2 and g(x) = (1x - 2)/(2x + 3) from x = -4.6 to x = -4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(-5x^2 + 4x - 4)) - 2 and g(x) = -4x - 1 between the vertical lines x = -0.0 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(2|x|) + 2)/(2(2|x|) + 2) and g(x) = -2x^2 + 2x + 5 from x = -1.2 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(2\u03c0(-1x^2 - 5x - 5)) - 2 and g(x) = (2x + 3)/(2x + 3) from x = 1.1 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(2cos(2\u03c0x + 3) + 1) - 2| - 2 and g(x) = -3x^2 - 1x + 1 from x = -0.7 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2\u03c0(1x + 3) + 3) + 2 and g(x) = 2x^2 + 4x + 3 between the vertical lines x = -1.3 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3cos(3\u03c0x + 3) + 2)^2 - 1(-3cos(3\u03c0x + 3) + 2) + 4 and g(x) = 2x^2 + 4x - 2 between the vertical lines x = 4.1 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(3|x + 2|), g(x) = (1x + 2)/(-2x - 3), x = -2.0, and x = -1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(2\u03c0(-4x^2 - 5x - 2) - 2) - 3 and g(x) = -1x^2 + 3x + 3 between the vertical lines x = 4.5 and x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3cos(2\u03c0x + 3))^2 - 4(-3cos(2\u03c0x + 3)) + 3 and g(x) = -2x - 3 between the vertical lines x = -3.2 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-1cos(1\u03c0x + 3) - 3) + 1| + 2 and g(x) = -1x + 1 from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-4x + 3) + 3|, g(x) = -1x + 1, x = 1.4, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((-2x + 2)/(-3x + 4)) - 1| + 1 and g(x) = -1x^2 - 4x - 1 from x = -0.3 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(4x - 4) - 1) - 1 and g(x) = 3x + 4 between the vertical lines x = -1.1 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-4x + 1) + 3| - 1 and g(x) = -4x^2 + 5x between the vertical lines x = 0.8 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(2\u03c0(-3|x - 1| - 3) - 3), g(x) = 1x^2 + 3x - 4, x = -3.7, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-2sin(1\u03c0x + 2) + 1) + 3)/(-3(-2sin(1\u03c0x + 2) + 1) + 2) and g(x) = 2x^2 - 2x - 3 between the vertical lines x = -2.6 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-2e^(2x) - 1) + 2| and g(x) = 1|x + 1| - 1 between the vertical lines x = -1.2 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1e^(2x))^2 - 4(-1e^(2x)) + 1 and g(x) = -1x - 3 between the vertical lines x = -4.0 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2cos(1\u03c0x + 3) + 3) - 2|, g(x) = -2|x| - 3, x = -0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(2|x + 2|) - 2| + 3 and g(x) = 2x^2 + 1x - 1 from x = -1.4 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1\u03c0((-3x + 3)/(-2x + 3)) + 1) + 1 and g(x) = -4x^2 - 1x between the vertical lines x = -0.1 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(1e^(-2x) - 2) and g(x) = 4x from x = -0.4 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(2\u03c0(-1x^2 + 1x - 1) + 1) - 2, g(x) = 5x + 4, x = -1.2, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(4x^2 - 2x - 2) - 3)/(3(4x^2 - 2x - 2) - 1), g(x) = -1|x - 1| - 1, x = -0.6, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-4x^2 - 4x + 4) + 2|, g(x) = -2x^2 + 2x + 1, x = -2.4, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2sin(2\u03c0x + 1) - 2) - 5, g(x) = -2x + 1, x = 4.0, and x = 4.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3\u03c0(-1x + 2)) - 2 and g(x) = -5x^2 - 4x - 2 between the vertical lines x = -0.6 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-2cos(3\u03c0x + 3) + 3) + 1| - 1 and g(x) = -5x - 2 from x = -1.2 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3((2x + 1)/(2x + 2)) - 2)/(-3((2x + 1)/(2x + 2)) + 1), g(x) = (1x - 2)/(3x - 2), x = 0.0, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0((-1x + 1)/(1x - 3)) - 1) + 1 and g(x) = 3|x + 2| - 3 from x = -3.0 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(5x^2 - 4x + 3)) - 3 and g(x) = 5x + 3 between the vertical lines x = -1.5 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(2\u03c0(-3|x - 2| - 1) - 1) + 2 and g(x) = -4x between the vertical lines x = -0.4 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(3cos(1\u03c0x + 3) + 1)^2 - 5(3cos(1\u03c0x + 3) + 1) + 3, g(x) = (2x)/(-3x), x = -1.5, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(3\u03c0(-3|x - 3|) - 3) + 1 and g(x) = -1x + 5 between the vertical lines x = 3.8 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(3\u03c0x - 1) + 2)^2 + 3(1sin(3\u03c0x - 1) + 2) + 4 and g(x) = 1|x + 2| - 3 from x = -2.6 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2cos(1\u03c0x - 1) + 3) - 3)/(-2(-2cos(1\u03c0x - 1) + 3) + 3), g(x) = -1x + 5, x = 1.9, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((3x - 1)/(3x + 3))^2 - 3((3x - 1)/(3x + 3)) + 1 and g(x) = (2x + 2)/(-1x - 1) from x = -0.4 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3e^(-1x) + 3)^2 - 2(-3e^(-1x) + 3) - 2, g(x) = -2|x - 3| + 3, x = -0.7, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-4x + 1) + 2| + 3 and g(x) = 3|x + 3| - 3 between the vertical lines x = 0.3 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(3x^2 - 1x - 2)| + 1 and g(x) = -1|x - 3| - 3 from x = -1.3 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0((-2x + 1)/(1x + 1)) - 2) and g(x) = 1x^2 + 1x - 4 from x = -2.9 to x = -2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2cos(3\u03c0x - 3) + 1) - 4, g(x) = 1x^2 - 5x - 5, x = 1.1, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-2cos(1\u03c0x) - 2)| - 3 and g(x) = (2x - 2)/(-3x - 2) from x = -0.4 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(-2(3x^2 - 1x - 1)) - 3, g(x) = (-1x + 1)/(-3x + 4), x = 0.7, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(5x^2 + 4x - 2) + 1| + 1 and g(x) = -1x - 5 between the vertical lines x = -1.3 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1\u03c0(-4x - 3) - 1) + 3 and g(x) = 3|x| between the vertical lines x = 0.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(2\u03c0(3x + 2) + 2) - 3 and g(x) = 1x - 5 from x = 3.4 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(5x^2 - 4x - 3)^2 + 4(5x^2 - 4x - 3) + 1 and g(x) = -3|x - 1| + 3 from x = 1.1 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(1|x| + 3) + 3) + 2 and g(x) = (3x - 2)/(3x + 1) between the vertical lines x = -1.7 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1((1x + 2)/(-1x - 3)) + 2)/(1((1x + 2)/(-1x - 3)) - 3) and g(x) = -3|x| between the vertical lines x = -2.8 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(3e^(1x) + 2) + 1)/(-2(3e^(1x) + 2) - 1) and g(x) = 3x^2 - 4x + 2 from x = 0.4 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(-4x - 3) + 2) - 2, g(x) = 1x^2 - 4x + 2, x = 2.1, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2x^2 - 3x + 5) + 3| + 1, g(x) = (-3x)/(-3x - 2), x = 1.4, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((-1x + 1)/(-3x + 2))^2 + 4((-1x + 1)/(-3x + 2)) and g(x) = -2|x - 3| between the vertical lines x = 0.6 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(5x^2 + 3x - 3) + 3| - 3 and g(x) = 5x - 4 between the vertical lines x = -1.2 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0(3x^2 - 2x - 4) - 2) + 1, g(x) = 1x - 5, x = 3.9, and x = 4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2sin(3\u03c0x - 1) - 3) - 4 and g(x) = -1|x - 2| - 3 between the vertical lines x = -1.0 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(-1|x - 1|) + 1) + 1 and g(x) = -2x^2 + 1x + 4 between the vertical lines x = 1.4 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(5x - 3)^2 + 4(5x - 3) and g(x) = (2x - 3)/(-1x - 1) between the vertical lines x = 0.6 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1|x - 1| + 3) - 2)/(-3(-1|x - 1| + 3) + 1) and g(x) = -1x + 1 between the vertical lines x = -1.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1sin(3\u03c0x - 2)) + 5 and g(x) = (2x + 1)/(-3x) between the vertical lines x = -0.3 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-5x + 5) - 2)/(-1(-5x + 5) + 2), g(x) = 1x - 1, x = 1.2, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2|x - 2| - 1) + 3, g(x) = 2x^2 - 3x, x = 0.8, and x = 2.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3\u03c0((3x + 2)/(-2x - 1)) + 3) + 2 and g(x) = -4x - 2 between the vertical lines x = -1.1 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(1|x + 3| - 1) - 3) - 1, g(x) = -2x^2 - 4x - 2, x = -1.0, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(1x + 2) - 3| + 1, g(x) = -2x^2 + 1x + 2, x = 0.5, and x = 1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0(2|x - 1| + 1) + 1) + 1 and g(x) = 3x^2 - 5x + 4 from x = 0.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-2cos(1\u03c0x + 3) + 1) + 3 and g(x) = 1x^2 - 3x - 3 between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((-3x - 1)/(3x + 3)) - 1|, g(x) = 1|x| - 1, x = -3.3, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-2cos(3\u03c0x - 2) + 2)^2 + 1(-2cos(3\u03c0x - 2) + 2) + 3 and g(x) = 5x - 4 from x = 2.8 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(2|x| - 2) + 3| - 2 and g(x) = (3x + 1)/(2x + 2) from x = -1.3 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-4x + 3) + 3)/(3(-4x + 3) - 2), g(x) = -3x - 2, x = -0.5, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-1x - 2)/(2x + 1))^2 - 5 and g(x) = 3|x| between the vertical lines x = -0.8 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(3|x + 2| - 1) + 2 and g(x) = -1x from x = -2.4 to x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2e^(1(2|x| - 3)) - 2 and g(x) = -1|x + 2| between the vertical lines x = -1.3 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-2sin(1\u03c0x - 2) + 1) - 1| - 2 and g(x) = -2|x + 3| + 2 from x = -2.0 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2e^(2x) + 1) - 2)/(-2(-2e^(2x) + 1) - 1) and g(x) = -2x + 4 from x = -0.2 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-3cos(1\u03c0x + 1) - 2) - 2)/(-3(-3cos(1\u03c0x + 1) - 2) - 1) and g(x) = 5x^2 + 4x + 2 from x = 2.4 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2sin(2\u03c0x - 2) + 1) - 1| - 2, g(x) = -3x^2 - 5x + 5, x = -2.4, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(2\u03c0(3|x - 2| + 1) + 2) - 3 and g(x) = -1x - 2 from x = 1.4 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0(-3|x - 1|) + 2) + 1, g(x) = -4x + 4, x = 0.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-5x - 4)^2 + 5(-5x - 4) - 4, g(x) = -4x^2 + 1x + 1, x = -0.8, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(3\u03c0(4x - 5) - 1) + 2 and g(x) = -2x - 2 between the vertical lines x = -1.7 and x = -1.5999999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1cos(3\u03c0x + 3) - 1) + 1, g(x) = -2x - 1, x = -0.9, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2cos(1\u03c0x - 3) + 1) - 4 and g(x) = -5x^2 - 2x - 5 between the vertical lines x = -0.6 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1sin(1\u03c0x) - 2) + 3 and g(x) = 3x^2 - 5x + 3 between the vertical lines x = 0.3 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(2x^2 - 1x - 2)| - 2, g(x) = (2x - 2)/(-3x - 3), x = 1.1, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((2x + 2)/(1x)) - 2)/(-3((2x + 2)/(1x)) + 1) and g(x) = (-1x - 2)/(2x + 3) between the vertical lines x = -1.6 and x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3((-1x - 1)/(2x + 1)) + 3)/(-3((-1x - 1)/(2x + 1)) + 4) and g(x) = -5x + 2 between the vertical lines x = -0.6 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1x^2 + 5x - 4)^2 - 5(-1x^2 + 5x - 4) - 1 and g(x) = (3x + 1)/(-1x + 2) from x = 2.5 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-1sin(1\u03c0x)) - 1 and g(x) = -2x - 3 from x = -1.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(1sin(3\u03c0x - 3) + 1) + 3| + 2, g(x) = -3x^2 + 1x + 5, x = -1.7, and x = 2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3\u03c0(3x + 2) + 3) - 2 and g(x) = (-3x)/(-3x + 4) between the vertical lines x = -3.9 and x = -3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-1cos(2\u03c0x + 2) - 3) - 2 and g(x) = 1|x + 3| - 1 from x = 4.0 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(-1(-3x + 3)) + 1 and g(x) = 3x + 3 from x = -0.7 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(5x^2 + 5x - 5)^2 - 5(5x^2 + 5x - 5) + 4, g(x) = -2x - 4, x = -0.7, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-1cos(1\u03c0x + 3)) + 5 and g(x) = -2|x + 1| + 2 between the vertical lines x = -1.2 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3\u03c0(5x^2 + 1x - 1) - 2) - 3 and g(x) = -1x^2 + 3x + 1 between the vertical lines x = 4.1 and x = 4.199999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(1\u03c0(4x^2 - 4x - 4) - 2) + 3, g(x) = 4x^2 - 2x, x = -0.6, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3\u03c0(4x - 4) - 3) + 3 and g(x) = -1x - 1 between the vertical lines x = -4.9 and x = -4.800000000000001. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1sin(1\u03c0x) + 2) - 1 and g(x) = (1x + 2)/(1x + 1) between the vertical lines x = -2.3 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(4x^2 - 1x) - 5, g(x) = (-3x + 1)/(-2x + 3), x = -0.4, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1x)^2 + 1(1x) + 5 and g(x) = -3|x - 1| + 1 from x = -2.4 to x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2|x + 3| - 3) + 1)/(2(2|x + 3| - 3) + 2) and g(x) = -3x^2 - 1x + 3 from x = -1.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2sin(3\u03c0x + 3) - 1) + 4, g(x) = 1x + 2, x = -0.3, and x = -0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-1x - 2)/(-3x + 4))^2 + 1 and g(x) = (2x - 1)/(1x - 3) from x = 0.5 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(1cos(3\u03c0x - 1) - 2) + 3| + 2, g(x) = -3x^2 - 3x - 4, x = -0.6, and x = -0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(-2|x + 3| - 3) + 2) - 3 and g(x) = (-1x + 3)/(1x + 3) between the vertical lines x = -4.7 and x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-3|x - 3| + 1)^2 - 4(-3|x - 3| + 1) + 2, g(x) = 2|x - 1| - 2, x = 2.3, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1\u03c0(-2x + 3) + 2) + 3 and g(x) = -1x + 1 between the vertical lines x = -2.2 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-5x^2 - 2x + 3) + 2) - 2, g(x) = 1|x - 2| - 3, x = 3.6, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(1\u03c0(-1x - 1) + 3) + 3 and g(x) = 3x^2 - 4x + 1 from x = 0.1 to x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(1x^2 - 3) - 1, g(x) = (2x - 1)/(-1x - 1), x = -0.2, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2x^2 + 3x + 5)^2 + 4(-2x^2 + 3x + 5) + 2 and g(x) = 3x - 2 between the vertical lines x = -1.2 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(2\u03c0(5x + 5) - 3), g(x) = (1x - 2)/(-2x + 1), x = 3.6, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(1\u03c0(-4x - 5) - 3) - 2 and g(x) = (-2x - 3)/(-3x - 3) from x = 4.8 to x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1\u03c0((-1x)/(3x - 2)) + 2) - 2 and g(x) = -1|x - 2| - 2 between the vertical lines x = 1.1 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(2\u03c0(-2|x - 2| + 3) + 3) + 3 and g(x) = (-2x - 3)/(-1x + 3) from x = -3.7 to x = -3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1|x - 3| + 1) - 1| + 1 and g(x) = -1x^2 + 1x + 1 from x = -3.0 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2cos(2\u03c0x + 1))^2 + 3(-2cos(2\u03c0x + 1)) - 2 and g(x) = 3x + 3 between the vertical lines x = -2.8 and x = -2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(3cos(3\u03c0x - 3) - 1)^2 + 4, g(x) = -3x, x = 3.6, and x = 3.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0(-1|x + 3| + 1) + 3) + 1 and g(x) = -2|x + 3| + 3 from x = -3.3 to x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-4x^2 + 2x + 2) - 1 and g(x) = 2|x - 2| - 2 from x = -0.1 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-4x - 4) + 2)/(3(-4x - 4) + 3), g(x) = -1x - 4, x = -4.4, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1x^2 - 1) - 3)/(3(-1x^2 - 1) + 1), g(x) = 2|x + 1| - 1, x = -1.3, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(3x^2 - 3x - 5) + 1)/(-2(3x^2 - 3x - 5) - 2), g(x) = (-2x + 2)/(1x - 3), x = -4.8, and x = -1.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-2|x - 2| - 1) - 2 and g(x) = -2|x| - 3 between the vertical lines x = 1.5 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2cos(1\u03c0x - 3))^2 + 5(2cos(1\u03c0x - 3)) - 4 and g(x) = 3x^2 - 1 between the vertical lines x = -1.0 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((-2x - 1)/(3x + 1))^2 + 4((-2x - 1)/(3x + 1)) + 1 and g(x) = 2|x + 2| - 3 from x = -3.7 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1e^(2x) + 3) and g(x) = 1x^2 + 3x - 5 from x = -2.6 to x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(1x + 2) - 1| + 1 and g(x) = -1x^2 - 1x + 3 between the vertical lines x = -3.0 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1x - 3) + 1)/(-2(1x - 3) + 3) and g(x) = 4x - 5 from x = 1.4 to x = 4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2sin(3\u03c0x - 1) + 2) + 2)/(1(2sin(3\u03c0x - 1) + 2) - 3) and g(x) = -4x^2 - 4x - 4 between the vertical lines x = 2.4 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-4x^2 - 4) - 3 and g(x) = (3x + 2)/(2x + 2) from x = 0.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(1sin(3\u03c0x - 3) - 1) - 2| + 1, g(x) = 5x^2 - 5x - 2, x = -0.8, and x = 1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0(1x^2 - 5x + 3) + 3) - 1 and g(x) = -4x^2 + 3x - 1 between the vertical lines x = 0.4 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1sin(3\u03c0x - 2) + 1) - 1)/(3(1sin(3\u03c0x - 2) + 1) + 3) and g(x) = 1x^2 - 3x - 5 from x = -1.1 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0(1x + 2) - 3) + 2 and g(x) = 1x + 4 between the vertical lines x = -1.6 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2sin(2\u03c0x) - 1) + 3)/(2(2sin(2\u03c0x) - 1) - 1) and g(x) = 3x^2 - 1x + 5 between the vertical lines x = -2.9 and x = -2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-2x - 3)^2 - 5, g(x) = -1|x| - 1, x = -1.8, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0((-1x - 1)/(3x - 2)) + 2) + 3 and g(x) = 1|x + 3| + 2 between the vertical lines x = 0.8 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-2cos(3\u03c0x + 1) - 2) + 2, g(x) = -4x, x = -4.2, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0(-5x) + 1) + 3, g(x) = -4x^2 + 3x + 1, x = 0.4, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3x^2 - 1x)^2 - 5(3x^2 - 1x) + 5, g(x) = (1x - 2)/(-2x + 3), x = 0.8, and x = 1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(1|x + 2| + 1) - 2) + 2, g(x) = (-2x + 2)/(-2x - 3), x = -4.2, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(2\u03c0((-2x + 3)/(-2x - 2))) - 1, g(x) = (2x - 3)/(-2x - 1), x = -2.1, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0(-1x^2 - 2x + 3) - 3) + 1, g(x) = (-1x - 2)/(1x - 3), x = -4.2, and x = -4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((3x + 3)/(3x - 1))^2 + 5((3x + 3)/(3x - 1)) - 5 and g(x) = 1x^2 + 1x - 2 between the vertical lines x = 0.8 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(-2|x + 3| - 1) - 2) + 3 and g(x) = 5x^2 - 3x between the vertical lines x = 0.9 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(5x - 3)^2 + 5(5x - 3) + 3 and g(x) = 1|x - 2| between the vertical lines x = 0.6 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3\u03c0((-1x - 2)/(3x - 2)) - 2) - 3 and g(x) = 1x^2 + 1x - 5 between the vertical lines x = 0.6 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|((3x)/(3x + 2))| - 1, g(x) = 1|x - 2| + 3, x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((1x + 1)/(1x)) + 4 and g(x) = 3|x + 3| from x = -4.6 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0(1x + 4) + 3) - 1, g(x) = 1x - 1, x = -0.2, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(3\u03c0((1x - 2)/(-2x - 1)) + 1) - 3 and g(x) = -3x + 1 from x = 0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2|x - 3| - 3) - 2)/(2(2|x - 3| - 3) + 3), g(x) = -2x^2 - 4x + 5, x = -2.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-2cos(1\u03c0x - 3) - 3) + 2)/(1(-2cos(1\u03c0x - 3) - 3)) and g(x) = (1x - 1)/(-1x - 2) from x = -4.3 to x = -3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(2(5x + 5)) and g(x) = (2x + 3)/(-2x - 2) from x = -1.5 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(4x + 1)^2 + 5(4x + 1), g(x) = -2x - 2, x = -1.6, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0((2x + 3)/(-3x + 4)) - 1) + 3, g(x) = 3|x| + 1, x = 0.3, and x = 0.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(5x + 3) + 3| - 3 and g(x) = -3x^2 + 2x + 5 between the vertical lines x = -1.3 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2sin(2\u03c0x) + 2)^2 - 4(-2sin(2\u03c0x) + 2) + 1 and g(x) = 1|x + 1| - 2 between the vertical lines x = 0.4 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1e^(-1x) - 2)^2 - 3(1e^(-1x) - 2) - 3, g(x) = -2x^2 + 4x - 2, x = -1.1, and x = -0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2x^2 - 2x)^2 - 3(2x^2 - 2x) - 2, g(x) = 1x - 4, x = -0.2, and x = 1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(3|x - 1| + 3) - 2, g(x) = -3|x + 3| - 3, x = 0.7, and x = 1.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3\u03c0(-1|x - 2| + 3) - 2) + 1 and g(x) = 2|x + 3| + 3 between the vertical lines x = -3.4 and x = -2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(5x^2 + 2x - 2) + 3)/(2(5x^2 + 2x - 2) - 3) and g(x) = (-1x)/(2x + 3) from x = -1.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(1\u03c0((1x - 2)/(3x + 1)) + 2) + 1 and g(x) = (-2x - 3)/(2x - 3) from x = -0.4 to x = -0.30000000000000004. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0(3x - 1) - 2) + 1 and g(x) = 2|x + 1| from x = -2.0 to x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3|x - 1| + 3) and g(x) = 1x^2 - 1x - 5 between the vertical lines x = -0.3 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(3\u03c0(-3x^2 - 1x - 4) - 2) + 3 and g(x) = 4x^2 + 1x + 2 between the vertical lines x = 0.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(1\u03c0(-4x^2 + 4x - 4) + 3) - 1 and g(x) = (3x)/(-1x - 1) from x = 1.9 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3|x| - 2) - 2 and g(x) = -2x - 5 from x = -0.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0((-3x + 2)/(-1x + 2)) - 1) - 1 and g(x) = (-2x + 1)/(-2x) between the vertical lines x = 1.9 and x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2cos(1\u03c0x + 3) - 1) - 1)/(1(-2cos(1\u03c0x + 3) - 1) + 1) and g(x) = (1x)/(-1x - 1) between the vertical lines x = 0.2 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(3sin(1\u03c0x) - 1)^2 + 3(3sin(1\u03c0x) - 1) and g(x) = (-1x + 2)/(2x + 3) from x = 2.9 to x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(4x^2 - 3x - 3) - 2 and g(x) = -5x - 1 between the vertical lines x = -0.5 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(2\u03c0((-2x + 2)/(3x)) + 3) - 1, g(x) = (-2x - 1)/(1x), x = -0.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(5x^2 - 3x - 5) - 2) - 1, g(x) = -1x^2 - 3x - 1, x = -2.2, and x = -2.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2sin(3\u03c0x) + 2)^2 + 1(-2sin(3\u03c0x) + 2) + 3, g(x) = (3x + 3)/(1x + 3), x = -4.6, and x = -4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0((-2x - 2)/(-1x)) + 2) + 2, g(x) = 5x^2 + 1x + 2, x = -0.0, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((-2x + 3)/(1x + 3)) + 1| - 2, g(x) = -3x^2 - 1x + 5, x = -0.3, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0((-2x + 2)/(1x + 1)) + 3), g(x) = (-2x - 3)/(-2x - 1), x = -1.4, and x = -1.2999999999999998. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2\u03c0(2x + 1) + 2) + 1 and g(x) = (2x + 3)/(-3x + 4) between the vertical lines x = 4.1 and x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3|x + 1|) + 4 and g(x) = (-1x - 3)/(1x + 2) between the vertical lines x = -1.8 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(5x - 2)^2 + 4(5x - 2) - 4, g(x) = -4x - 3, x = -0.0, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(3\u03c0((3x + 3)/(1x + 2)) - 2) + 1 and g(x) = -1x^2 + 4x + 4 from x = -0.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(4x^2 - 4) - 4 and g(x) = -2|x + 2| between the vertical lines x = -1.1 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-2x + 3) - 3, g(x) = (-3x - 1)/(3x - 1), x = 0.1, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(3\u03c0(1|x - 2| + 3) + 2), g(x) = -2x^2 - 5x + 3, x = -3.0, and x = 0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1sin(2\u03c0x - 2))^2 + 2(-1sin(2\u03c0x - 2)), g(x) = -3x^2 + 4, x = -0.8, and x = 0.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3sin(1\u03c0x - 1) + 3))/(-2(-3sin(1\u03c0x - 1) + 3) - 3) and g(x) = (1x - 1)/(-1x + 3) between the vertical lines x = 0.7 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-5x^2 + 1x + 1) and g(x) = 4x + 3 between the vertical lines x = -0.4 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2x - 2)^2 - 2(-2x - 2) + 5 and g(x) = -5x^2 - 1x + 4 between the vertical lines x = -1.9 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(-2|x - 3| - 2) + 3) - 3 and g(x) = (2x - 1)/(1x + 2) between the vertical lines x = -1.3 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0((2x)/(3x - 2)) - 2) - 2 and g(x) = -1|x - 2| - 3 from x = 1.3 to x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-2cos(2\u03c0x + 1) + 1)^2 + 4(-2cos(2\u03c0x + 1) + 1) - 1, g(x) = (2x - 2)/(1x + 2), x = -0.3, and x = -0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(3\u03c0(1x + 1) + 2) + 2 and g(x) = -5x - 5 from x = -1.5 to x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(1(1|x + 1| - 2)) - 2 and g(x) = -5x^2 + 5 from x = -1.2 to x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2sin(1\u03c0x + 3))^2 - 2(2sin(1\u03c0x + 3)) - 2 and g(x) = 3|x - 1| - 2 between the vertical lines x = 2.2 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(2(-3|x - 2| + 1)) + 2 and g(x) = -1x^2 + 2x + 4 between the vertical lines x = -0.7 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(3|x - 1| - 2) + 2)/(1(3|x - 1| - 2) + 1), g(x) = 3|x - 2| + 3, x = 0.5, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(-2((2x)/(-3x))) - 1 and g(x) = 1|x - 3| + 1 between the vertical lines x = 1.2 and x = 4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2|x| - 2) + 2)/(-3(2|x| - 2) + 2) and g(x) = 1x + 1 between the vertical lines x = -0.7 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((-1x + 1)/(1x + 1)) - 3 and g(x) = -1x^2 + 4x - 1 between the vertical lines x = 0.2 and x = 4.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2cos(3\u03c0x + 3) + 1) + 2 and g(x) = 2|x| - 2 between the vertical lines x = 3.6 and x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(4x - 1)^2 + 2(4x - 1) + 4 and g(x) = 2x^2 - 5x + 3 between the vertical lines x = 0.1 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(2|x - 2|)^2 + 3(2|x - 2|) and g(x) = 1x^2 - 1x - 4 between the vertical lines x = 0.0 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((-1x - 3)/(3x + 1))^2 + 5((-1x - 3)/(3x + 1)) + 5, g(x) = (-3x - 1)/(-2x - 3), x = -1.9, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1((-2x)/(1x + 1)) - 3)/(-3((-2x)/(1x + 1)) + 4) and g(x) = -1x^2 + 3x - 1 between the vertical lines x = 0.1 and x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(1\u03c0(1|x - 1| + 1) + 3) + 2 and g(x) = 1x - 1 between the vertical lines x = 2.3 and x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3|x - 3| + 2)^2 + 3(3|x - 3| + 2) and g(x) = -2x^2 - 5x - 3 from x = 2.6 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2\u03c0(-2x - 5) + 2) and g(x) = (-3x + 1)/(3x + 3) between the vertical lines x = 2.4 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0((2x + 3)/(-2x)) - 3) - 3, g(x) = -1x^2 - 1x - 1, x = 0.7, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(3|x - 3| - 2) - 1)/(-1(3|x - 3| - 2) + 2), g(x) = (3x)/(-2x - 1), x = 2.2, and x = 3.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0((-2x - 2)/(-1x - 1)) - 2) - 3 and g(x) = 4x^2 - 5x - 5 from x = -0.2 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(2|x - 3| - 1) + 2)/(3(2|x - 3| - 1) - 1) and g(x) = 1x^2 - 4x + 3 from x = 1.3 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-2x - 3)/(-1x - 3))^2 + 5((-2x - 3)/(-1x - 3)) - 5 and g(x) = -1|x - 1| - 3 from x = -2.1 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-1x)/(-2x + 3)) + 2)/(-2((-1x)/(-2x + 3)) - 1), g(x) = -1|x| + 3, x = 1.1, and x = 3.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-2sin(2\u03c0x + 1) + 1) - 2)/(-2(-2sin(2\u03c0x + 1) + 1) - 3), g(x) = (-2x + 3)/(3x - 2), x = 3.0, and x = 3.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-5x^2 - 1x + 3)^2 - 3(-5x^2 - 1x + 3) and g(x) = -1x^2 - 4x + 2 from x = -1.0 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(5x^2 + 1x - 1) + 4 and g(x) = -5x - 4 between the vertical lines x = -1.0 and x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-2x + 1)/(-3x + 1))^2 + 5((-2x + 1)/(-3x + 1)) and g(x) = (-3x + 2)/(-3x + 1) between the vertical lines x = 0.2 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(1|x - 2| - 3) - 5, g(x) = (-2x - 3)/(2x + 2), x = -2.1, and x = -0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(5x^2 + 4x + 2))/(-3(5x^2 + 4x + 2) - 1) and g(x) = -1|x + 1| + 3 from x = -3.0 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(3cos(1\u03c0x + 1)) - 4, g(x) = (-2x + 2)/(-2x + 3), x = -4.6, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1e^(-1x) + 2) - 1)/(-1(-1e^(-1x) + 2) - 3) and g(x) = 1x^2 - 5x + 4 between the vertical lines x = -1.5 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(1x + 2) - 2)/(-3(1x + 2) + 2) and g(x) = 1x + 1 between the vertical lines x = -2.0 and x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1x^2 - 4x - 4)^2 - 1(1x^2 - 4x - 4) - 2 and g(x) = 5x + 4 between the vertical lines x = -1.1 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-5x^2 - 2)^2 - 3(-5x^2 - 2) + 3 and g(x) = 1x^2 - 1x - 1 between the vertical lines x = -0.6 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1((-3x - 3)/(1x + 2)) + 2)/(-2((-3x - 3)/(1x + 2)) - 1), g(x) = 1x^2 - 1x - 5, x = -0.9, and x = 2.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-1x) + 1| - 3 and g(x) = 1x^2 - 3x + 2 from x = 2.0 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-5x^2 + 5x + 1) + 1)/(1(-5x^2 + 5x + 1) - 3), g(x) = 1x - 1, x = -0.1, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((1x - 2)/(2x - 1)) + 1 and g(x) = 2x + 2 from x = -1.4 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(-1|x + 1| + 3) - 1) - 3 and g(x) = -2x^2 - 4x + 4 between the vertical lines x = -3.0 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(4x^2 - 2x - 3)^2 - 2, g(x) = -5x^2 + 4x + 2, x = -0.9, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-1|x - 3| + 2) + 5, g(x) = (-2x)/(-3x - 3), x = -0.9, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-2sin(1\u03c0x + 2)) - 3, g(x) = (-2x - 2)/(1x), x = -3.7, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(3cos(3\u03c0x - 1) + 1) + 1| - 3, g(x) = -5x - 3, x = -0.7, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(2\u03c0(-3x + 1) + 3) + 2 and g(x) = 4x^2 + 3x + 1 from x = -1.1 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-3x - 2) + 3| - 3 and g(x) = -1|x| - 1 between the vertical lines x = 0.0 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(2\u03c0(1|x + 3| + 1) - 1) + 1, g(x) = -4x + 1, x = -0.1, and x = 0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(1((-3x - 2)/(1x + 1))) - 2, g(x) = 2|x - 3| - 3, x = -0.8, and x = 2.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0(-4x^2 - 1x - 4) + 1) + 3, g(x) = 1x^2 + 4x + 5, x = -3.7, and x = -3.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2e^(1x) + 2) + 1)/(2(-2e^(1x) + 2) + 1) and g(x) = 4x^2 - 5x + 1 between the vertical lines x = 0.0 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(3\u03c0(1|x - 3| + 3) - 1) + 2 and g(x) = (-2x)/(-3x - 3) from x = -2.6 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(3\u03c0((-1x - 3)/(2x + 1)) - 1) + 2, g(x) = -1x^2 + 4x - 1, x = 0.8, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(1\u03c0((1x - 2)/(-1x + 2)) + 3) - 2 and g(x) = 3x^2 - 3x - 3 between the vertical lines x = -0.2 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((-3x - 1)/(-3x - 2)) - 4 and g(x) = (1x + 2)/(-1x - 3) between the vertical lines x = -2.4 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(3\u03c0(-3x + 2) - 1) and g(x) = -4x + 4 from x = 0.9 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1sin(3\u03c0x - 1)) - 2)/(-1(-1sin(3\u03c0x - 1)) - 2) and g(x) = 3x + 1 from x = -0.2 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-2|x + 1| + 3) + 5 and g(x) = (3x)/(2x - 1) from x = -0.1 to x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-1x - 2)/(-2x - 2)) - 2 and g(x) = -3|x + 1| + 2 between the vertical lines x = -0.8 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|x + 2| - 3) + 3)/(2(-3|x + 2| - 3)) and g(x) = 4x^2 - 3 from x = -0.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(2sin(3\u03c0x - 1) + 3) + 2)/(3(2sin(3\u03c0x - 1) + 3) - 2), g(x) = (-3x + 2)/(2x + 1), x = 0.8, and x = 0.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1((2x - 3)/(1x + 1)) + 1)/(3((2x - 3)/(1x + 1))) and g(x) = 1x^2 + 1x - 1 from x = -1.5 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0(-3x - 4) - 1) - 2, g(x) = -3|x - 3| + 2, x = 1.5, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-3sin(2\u03c0x + 1) + 2)| - 3, g(x) = -1|x + 3| + 2, x = 1.1, and x = 1.2000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(2\u03c0(-5x^2 - 2x - 4) + 1) + 3, g(x) = -3|x + 3| + 3, x = -3.0, and x = -2.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-2sin(1\u03c0x - 3) + 3)^2 - 4(-2sin(1\u03c0x - 3) + 3) + 4 and g(x) = 5x^2 + 3x + 1 between the vertical lines x = -2.0 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-2sin(3\u03c0x + 1) + 2) - 3|, g(x) = 2x^2 - 3x + 2, x = 2.2, and x = 2.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(3\u03c0(1x^2 - 4x + 1) + 2) + 1 and g(x) = (3x + 1)/(-1x - 2) between the vertical lines x = -0.6 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2cos(2\u03c0(3|x| + 1) + 1) - 1 and g(x) = -1x + 1 from x = 3.8 to x = 3.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2cos(3\u03c0x - 1) - 3) + 2| + 1 and g(x) = -3x^2 - 4x between the vertical lines x = -1.7 and x = -1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(3\u03c0((-3x - 1)/(-3x)) + 1) and g(x) = 1x^2 - 2x - 2 between the vertical lines x = -0.5 and x = 2.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-1x^2 + 3x - 4)^2 - 5(-1x^2 + 3x - 4) and g(x) = -4x - 1 from x = 1.1 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2|x - 3| - 3))/(-2(2|x - 3| - 3) + 1) and g(x) = -1x - 3 from x = -3.5 to x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(3|x + 3| - 2)^2 + 4(3|x + 3| - 2), g(x) = (1x - 3)/(-1x - 1), x = -3.5, and x = -2.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(-5x + 3)) + 3 and g(x) = 3|x - 2| between the vertical lines x = 2.8 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1cos(2\u03c0(-2|x + 3|) - 2) + 1, g(x) = 3|x + 2|, x = -2.1, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3sin(3\u03c0x - 2) - 1) - 2| + 1 and g(x) = 2x^2 + 1x - 3 between the vertical lines x = -0.7 and x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2sin(3\u03c0x + 3)) - 5 and g(x) = 5x - 5 between the vertical lines x = 0.0 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-2sin(1\u03c0x) - 2))/(2(-2sin(1\u03c0x) - 2) + 3), g(x) = (-1x - 2)/(-3x + 2), x = -0.7, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(2\u03c0(-4x^2 - 4x + 2) + 2), g(x) = (1x - 3)/(-2x), x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(4x^2 + 3x) - 1)/(-1(4x^2 + 3x) + 3), g(x) = (1x + 1)/(-2x - 3), x = -0.7, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(-2|x - 1| + 3) - 2) - 3, g(x) = 1x^2 + 4x + 3, x = -2.3, and x = -2.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(3cos(1\u03c0x - 2) + 3)^2 + 1(3cos(1\u03c0x - 2) + 3) - 2, g(x) = -5x, x = 3.2, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(2\u03c0(-2x^2 - 3x + 1) - 2) - 1, g(x) = 1x + 4, x = -4.1, and x = -4.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(4x - 1) + 1 and g(x) = (1x - 3)/(1x - 2) between the vertical lines x = 0.3 and x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1x - 1) + 1)/(3(-1x - 1)) and g(x) = -3x^2 + 1x + 1 from x = -0.2 to x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-2x + 1)/(3x + 1)) - 1 and g(x) = 1x + 2 from x = -3.8 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(3\u03c0((1x - 3)/(2x + 2)) + 3) + 3, g(x) = 1|x + 3| - 2, x = -0.8, and x = -0.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-5x^2 - 3x) - 3| - 1 and g(x) = 3|x + 3| - 3 from x = -0.5 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(2\u03c0(-4x - 3) + 3) - 1 and g(x) = -3x^2 + 4x - 5 from x = 0.8 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(4x + 4) - 2)/(-3(4x + 4) - 3), g(x) = -2x^2 + 2x + 1, x = -1.3, and x = -0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-2|x + 2| + 2) - 1| and g(x) = -1|x + 3| - 3 between the vertical lines x = -3.0 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1\u03c0(-1x - 2) - 3) + 1 and g(x) = -1x - 2 between the vertical lines x = -5.0 and x = -4.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1x)/(2x - 1))^2 + 2((1x)/(2x - 1)) + 4 and g(x) = 1x^2 - 3x - 3 between the vertical lines x = -1.6 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(2cos(2\u03c0x + 3) + 1) - 2 and g(x) = -3x + 4 from x = 3.4 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(1\u03c0((-2x - 1)/(1x)) + 1) - 1 and g(x) = 3x^2 + 3x - 2 between the vertical lines x = 0.2 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(2cos(2\u03c0x - 2))^2 - 5(2cos(2\u03c0x - 2)) + 3, g(x) = (2x - 2)/(2x + 1), x = 3.5, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(1x^2 - 3x - 1)) - 2, g(x) = -3x + 5, x = 2.1, and x = 2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(4x)^2 - 2(4x) - 3 and g(x) = 1|x - 2| - 3 between the vertical lines x = -0.2 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((1x - 2)/(-2x + 3))| - 1 and g(x) = (3x - 1)/(-3x + 2) from x = 0.8 to x = 1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(2cos(2\u03c0x + 1) - 1) + 3)/(-3(2cos(2\u03c0x + 1) - 1)), g(x) = -1x + 4, x = -0.3, and x = 0.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(3cos(1\u03c0x) - 1) + 3, g(x) = -5x^2 - 4x + 2, x = -0.4, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3x)^2 + 3(-3x) and g(x) = -1|x| + 1 from x = -1.0 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2x + 1)/(1x - 3))^2 - 5((-2x + 1)/(1x - 3)) - 5 and g(x) = -2|x - 1| + 3 between the vertical lines x = -0.6 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((2x - 1)/(-2x - 3))^2 - 1((2x - 1)/(-2x - 3)) - 2 and g(x) = 4x^2 + 4x - 5 between the vertical lines x = -2.5 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(2\u03c0(-1|x - 2|)) + 3 and g(x) = -4x - 1 from x = -1.6 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-2x^2 + 2x - 5) + 3| + 1 and g(x) = 5x^2 + 1 from x = -4.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3((-1x - 2)/(-1x)))/(-3((-1x - 2)/(-1x)) - 1) and g(x) = -2x - 2 from x = -1.7 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2|x + 3|) + 2)/(-2(-2|x + 3|) - 3), g(x) = 2x - 4, x = -3.8, and x = -2.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-2x^2 + 3x)^2 + 4(-2x^2 + 3x) - 5 and g(x) = -1|x - 1| from x = -0.4 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2e^(1x) + 3)^2 + 5(-2e^(1x) + 3) + 5 and g(x) = 1|x + 2| - 2 between the vertical lines x = -0.4 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2cos(1\u03c0x + 3) - 3)^2 + 1(-2cos(1\u03c0x + 3) - 3) - 3 and g(x) = 2x - 2 between the vertical lines x = -4.1 and x = -3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2e^(1(2x^2 - 4x + 3)) + 2, g(x) = -2x - 2, x = 0.8, and x = 1.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-1sin(3\u03c0x + 1))^2 - 5(-1sin(3\u03c0x + 1)) + 1, g(x) = -3|x - 1| - 1, x = 1.0, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1cos(3\u03c0x - 2) - 1) + 3 and g(x) = 5x^2 - 2x - 5 between the vertical lines x = -1.1 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3e^(-2(-1x^2 - 2x + 2)) - 3, g(x) = (-3x + 1)/(-2x), x = 0.1, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(2\u03c0(1|x - 1| + 2) + 1) - 2 and g(x) = (2x - 1)/(-3x - 3) between the vertical lines x = -2.7 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(1\u03c0(2|x - 1|) - 2) + 3, g(x) = 2|x + 2| - 3, x = 2.2, and x = 2.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(3\u03c0(4x^2 - 4x + 2) + 3) + 3, g(x) = (-1x + 2)/(-1x - 1), x = -3.6, and x = -3.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(5x^2 + 5x - 3) + 1| - 1, g(x) = -5x - 4, x = -1.6, and x = -1.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(2x^2 - 2) + 1) - 1 and g(x) = -2|x + 2| + 1 between the vertical lines x = -2.8 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-2|x - 3|)^2 + 3(-2|x - 3|) + 3 and g(x) = (-3x - 1)/(3x + 2) from x = 2.5 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(4x^2 - 4x - 3)^2 + 4(4x^2 - 4x - 3) + 2 and g(x) = (-2x + 2)/(-3x - 1) between the vertical lines x = -0.6 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-3x + 1)^2 + 4(-3x + 1) - 3 and g(x) = 2|x| - 3 between the vertical lines x = 0.3 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3sin(3\u03c0x + 2)))/(1(3sin(3\u03c0x + 2)) + 1) and g(x) = (2x)/(-1x - 1) from x = 3.5 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(3\u03c0((-2x - 1)/(1x - 2)) + 3) + 3, g(x) = 4x^2 - 2x - 4, x = 1.6, and x = 1.7000000000000002. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-3sin(1\u03c0x - 2) + 1) + 2 and g(x) = -2|x - 2| + 3 from x = 2.8 to x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2sin(2\u03c0x + 3) + 2)^2 - 1(2sin(2\u03c0x + 3) + 2) - 3 and g(x) = -1x^2 - 5x between the vertical lines x = -0.0 and x = 0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(2\u03c0((1x - 2)/(2x - 3)) - 3) + 1 and g(x) = 1|x + 1| between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(3cos(2\u03c0x - 3) - 3) + 2, g(x) = 2x^2 - 2x + 5, x = -2.2, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-5x^2 - 2x + 1) + 4 and g(x) = -5x^2 - 3x between the vertical lines x = -0.4 and x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1x + 3) - 3)/(3(-1x + 3) - 1), g(x) = 1x^2 - 5x + 2, x = 2.5, and x = 4.7. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(2\u03c0(-3|x - 2| + 3) - 3) + 3 and g(x) = 2x + 5 between the vertical lines x = -1.7 and x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(1\u03c0(2|x| + 3) - 1) - 3 and g(x) = (3x + 3)/(-3x + 2) from x = 2.3 to x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-3cos(3\u03c0x + 2) + 1))/(-3(-3cos(3\u03c0x + 2) + 1) + 1) and g(x) = -3|x - 2| + 2 between the vertical lines x = 0.3 and x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1sin(2\u03c0x + 1) - 1) - 5 and g(x) = -3x^2 + 1x - 2 between the vertical lines x = -1.5 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3sin(2\u03c0x) + 3)^2 + 5(-3sin(2\u03c0x) + 3) - 3 and g(x) = -3|x + 1| - 2 between the vertical lines x = -0.8 and x = -0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1cos(2\u03c0x + 2) - 1) + 2 and g(x) = 3x^2 + 5x + 5 between the vertical lines x = -1.4 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(3sin(1\u03c0x - 1)) - 3)/(3(3sin(1\u03c0x - 1)) + 1) and g(x) = 2|x + 2| + 1 from x = -0.6 to x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-3x^2 + 2x))/(-1(-3x^2 + 2x) + 2), g(x) = -1|x - 3| - 1, x = 1.8, and x = 4.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((2x + 1)/(1x))^2 - 2 and g(x) = -3|x - 1| - 3 between the vertical lines x = -0.2 and x = 2.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2|x + 1| + 1) - 1)/(3(2|x + 1| + 1) + 3) and g(x) = 1x^2 + 1x - 3 between the vertical lines x = -2.1 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(2\u03c0(-1x + 3) - 3) - 1 and g(x) = (3x + 2)/(-2x + 3) from x = -1.8 to x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(3\u03c0(-1|x - 3| - 3) - 1) - 3 and g(x) = -1x^2 + 5x - 5 from x = 0.2 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-2(1x + 2)) - 1 and g(x) = -5x^2 + 3 between the vertical lines x = -0.9 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0(-3x - 1) - 2) - 2 and g(x) = -1x + 2 from x = 4.3 to x = 4.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2cos(3\u03c0x - 2) - 2) - 2| + 1 and g(x) = -1|x - 2| + 2 from x = -2.0 to x = -1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(1x - 5) + 2| - 2 and g(x) = (3x)/(3x + 2) between the vertical lines x = -0.8 and x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-1sin(2\u03c0x - 3) - 2) + 1)/(-2(-1sin(2\u03c0x - 3) - 2) - 1) and g(x) = -3x^2 + 1x + 2 between the vertical lines x = -1.0 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0((2x - 2)/(1x + 2)) + 2) + 1 and g(x) = (2x - 2)/(-3x - 2) between the vertical lines x = -0.4 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(2\u03c0(-1x - 5) + 1) - 2 and g(x) = 3|x - 3| - 2 from x = 3.2 to x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-2x - 1)/(-2x + 1))^2 + 3((-2x - 1)/(-2x + 1)) - 3 and g(x) = 3|x - 2| from x = 0.2 to x = 4.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(3\u03c0((2x + 3)/(1x - 2)) - 2) - 2 and g(x) = (2x + 2)/(3x - 2) from x = -0.6 to x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(-3x^2 + 4x + 3) + 1| - 2 and g(x) = (-3x + 2)/(3x - 2) from x = 2.0 to x = 2.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3x^2 + 4) + 3)/(-1(-3x^2 + 4) - 3) and g(x) = -2x^2 + 1x - 2 between the vertical lines x = -1.4 and x = 1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(3\u03c0(1|x - 2| + 3)) + 2, g(x) = 4x^2 - 4x - 1, x = -0.6, and x = 1.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2\u03c0(-2x + 4) - 3) - 2 and g(x) = -3x + 3 between the vertical lines x = 1.4 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1cos(2\u03c0x - 2) - 1)^2 - 5(1cos(2\u03c0x - 2) - 1) - 4 and g(x) = (2x)/(-1x - 2) between the vertical lines x = -4.8 and x = -4.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(3\u03c0(2x + 3) + 2), g(x) = 1x^2 - 4x + 1, x = 1.0, and x = 3.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-2x - 1) - 2| - 1 and g(x) = -1|x| + 2 from x = -2.0 to x = 0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|x + 3|)^2 + 2 and g(x) = -1x between the vertical lines x = -3.4 and x = -2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(1x^2 + 2x) - 3, g(x) = 2x^2 + 1x - 1, x = -1.2, and x = -0.3. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1cos(3\u03c0x + 3) + 3) - 1)/(2(-1cos(3\u03c0x + 3) + 3) - 3) and g(x) = -3|x| from x = -1.0 to x = -0.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((-2x - 2)/(-1x + 3)) - 1)/(-3((-2x - 2)/(-1x + 3)) + 4), g(x) = -1x^2 - 5x - 3, x = -4.8, and x = -0.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-2|x + 2| + 1))/(-3(-2|x + 2| + 1) - 2), g(x) = -1x^2 + 3x + 4, x = -2.8, and x = 4.1. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1((3x + 3)/(3x + 1)) + 3)/(-1((3x + 3)/(3x + 1)) - 1), g(x) = 3x - 1, x = -0.9, and x = 0.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(4x^2 - 1x + 3) - 1)/(-1(4x^2 - 1x + 3) - 3) and g(x) = -2|x + 1| + 3 between the vertical lines x = -1.3 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(1\u03c0(-3x^2 + 5x + 1) + 2) + 1, g(x) = -1x - 3, x = -1.6, and x = -1.5. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(1sin(3\u03c0x + 3) - 2)^2 + 4(1sin(3\u03c0x + 3) - 2) - 5, g(x) = -2x^2 - 1x - 3, x = -2.0, and x = 1.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2|x + 1| - 3) + 1, g(x) = 2|x - 1| + 2, x = -4.5, and x = 0.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(-3x^2 + 1x - 5) - 1) + 2 and g(x) = 4x^2 - 1x - 3 from x = 1.3 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-3sin(2\u03c0x + 1) + 1) - 3)/(-2(-3sin(2\u03c0x + 1) + 1) - 2), g(x) = 2x + 5, x = -4.0, and x = -3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-1x^2 + 3x + 5)| - 3, g(x) = (3x)/(1x + 2), x = 3.7, and x = 4.6. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4x - 3) + 1)/(-2(-4x - 3) - 2) and g(x) = 5x + 5 between the vertical lines x = -1.0 and x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-3sin(2\u03c0x) + 2) + 3)/(1(-3sin(2\u03c0x) + 2) - 3) and g(x) = (-3x)/(1x - 2) from x = -1.6 to x = -0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3e^(1x)))/(1(-3e^(1x)) + 1) and g(x) = 3x^2 - 2x - 2 from x = -0.2 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(2x^2 + 2x - 2)^2 - 3(2x^2 + 2x - 2) + 5 and g(x) = -4x from x = 0.2 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3sin(1\u03c0x - 2))^2 + 2(3sin(1\u03c0x - 2)) - 4 and g(x) = (2x + 3)/(-2x + 3) between the vertical lines x = -4.2 and x = -3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1x + 3) - 1 and g(x) = (1x - 3)/(3x - 2) between the vertical lines x = -4.5 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((3x - 3)/(-3x)) + 2| + 1, g(x) = -1|x - 3|, x = -0.3, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-3sin(2\u03c0x + 3) + 2) + 3, g(x) = 2|x - 2| - 1, x = 3.6, and x = 3.9. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(-1x^2 + 4x + 4) - 3) - 2 and g(x) = 1x^2 + 3x - 2 from x = -2.6 to x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-4x^2 + 2x + 2) - 3)/(-1(-4x^2 + 2x + 2) - 2) and g(x) = -1x + 1 from x = -0.5 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1|x + 2| - 2) + 3)/(3(1|x + 2| - 2) - 1) and g(x) = 2x - 1 from x = -0.4 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(1cos(1\u03c0x - 1) + 1) + 3| - 2, g(x) = -5x^2 - 3x, x = -2.1, and x = 1.2. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(2cos(2\u03c0x + 1)) + 2| + 1, g(x) = (1x - 3)/(-1x), x = -3.3, and x = -3.0. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-1cos(2\u03c0x + 2) + 2) - 3)/(-1(-1cos(2\u03c0x + 2) + 2) + 2) and g(x) = (-1x + 1)/(3x - 2) from x = -2.5 to x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2sin(3\u03c0x) + 1) + 2, g(x) = (-2x - 3)/(-2x + 3), x = 4.0, and x = 4.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(4x^2 - 1) + 2, g(x) = 5x + 1, x = -1.0, and x = 0.4. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3sin(1\u03c0x - 3))^2 + 2(3sin(1\u03c0x - 3)) - 5 and g(x) = -1x^2 - 1x between the vertical lines x = -0.2 and x = 1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2x^2 - 2x + 4)^2 - 2(-2x^2 - 2x + 4) - 2, g(x) = -1x^2 + 3x + 1, x = -2.3, and x = -1.8. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-1sin(2\u03c0x + 2) - 1) + 2| - 2 and g(x) = -2|x - 1| from x = -0.2 to x = -0.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.0", "dataset": "MATH"}