{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(4((-2(4x - 1))/(-1(4x - 1) + 2))^2 - 5((-2(4x - 1))/(-1(4x - 1) + 2)) + 2) + 3| and g(x) = -3(1|(-1x - 3) + 1| + 1)^2 + 3(1|(-1x - 3) + 1| + 1) - 3 from x = -1.3 to x = 0.5. Round 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(5(-3cos(2\u03c0x + 3) + 3)) - 2)/(1(5(-3cos(2\u03c0x + 3) + 3)) + 2) and g(x) = 5(-1x + 1)^2 + 4(-1x + 1) - 4 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1(1cos(3\u03c0x - 3) - 1)^2 + 1(1cos(3\u03c0x - 3) - 1) - 3) - 1 and g(x) = -1((-2x + 1)/(-2x))^2 - 5((-2x + 1)/(-2x)) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|(-3((-2(-3x - 4) + 2)/(-3(-3x - 4) - 3))^2 - 2((-2(-3x - 4) + 2)/(-3(-3x - 4) - 3)) - 5)| + 1, g(x) = 5(1(-1sin(2\u03c0x) - 2)^2 - 5(-1sin(2\u03c0x) - 2) - 3) - 1, 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": "6.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(-1|(2((-3x + 1)/(-1x - 1)) + 2) - 2|)^2 + 2(-1|(2((-3x + 1)/(-1x - 1)) + 2) - 2|) - 4 and g(x) = -1|(1(2sin(2\u03c0x))^2 + 4(2sin(2\u03c0x)) - 2) - 2| + 3 between the vertical lines x = 0.0 and 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) = 5(1|(1e^(2x) - 3) + 3| - 1)^2 - 3(1|(1e^(2x) - 3) + 3| - 1) - 4 and g(x) = 2(-2sin(2\u03c0x - 2)) - 1 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((1(1x - 4) + 3)/(-2(1x - 4))) - 3| and g(x) = -1(3x^2 + 2x + 4) + 5 between the vertical lines x = 0.9 and x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-4(3|(-2x^2 + 3x + 3) + 2| + 2) - 3))/(2(-4(3|(-2x^2 + 3x + 3) + 2| + 2) - 3)), g(x) = (2(-4(-3cos(1\u03c0x - 2) + 1)^2 - 4(-3cos(1\u03c0x - 2) + 1) + 3) + 1)/(-1(-4(-3cos(1\u03c0x - 2) + 1)^2 - 4(-3cos(1\u03c0x - 2) + 1) + 3) + 2), x = -3.6, 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-2(1|(-1x^2 - 2x + 1) + 2| - 3) - 3)/(-1(1|(-1x^2 - 2x + 1) + 2| - 3) - 1)) - 1 and g(x) = 3|(-3e^(-1(2x - 2)) - 3) + 1| - 2 from x = 0.4 to x = 1.4. 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": "Calculate the area enclosed between the functions f(x) = (2(-3(3cos(2\u03c0x + 3) + 1)^2 + 3(3cos(2\u03c0x + 3) + 1) + 1) + 2)/(-2(-3(3cos(2\u03c0x + 3) + 1)^2 + 3(3cos(2\u03c0x + 3) + 1) + 1) - 3) and g(x) = (-3(-1x + 4))/(2(-1x + 4) + 2) from x = 0.2 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) = 1|(-2((3(-3cos(3\u03c0x + 2) + 1) + 2)/(-3(-3cos(3\u03c0x + 2) + 1) + 2)) + 4) + 2| + 2, g(x) = -3sin(1\u03c0((1(-5x + 5) + 1)/(3(-5x + 5))) - 2), x = -2.1, 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": "19.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(3|(-2x + 3) + 1| - 1)) - 1 and g(x) = -3(3sin(3\u03c0x - 1) + 1) + 3 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(1((2(1|x + 1| + 1) + 1)/(1(1|x + 1| + 1)))) - 3 and g(x) = (3(-2|x + 3| + 1) + 3)/(3(-2|x + 3| + 1) + 2) between the vertical lines x = -3.8 and x = -2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((-1(-1|x| - 2) - 3)/(-3(-1|x| - 2) - 1)) + 4, g(x) = 3cos(3\u03c0(1x - 4)) + 1, 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(2\u03c0((-2(-1x^2 + 2x) + 2)/(-1(-1x^2 + 2x) + 3)) - 2) and g(x) = 5(2x^2 + 1x - 5) - 5 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": "70.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(-1(-3|x + 3| - 3)^2 + 5(-3|x + 3| - 3) + 2) - 1) - 1 and g(x) = -1e^(-1(-3|x - 1| + 3)) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1(3|x - 2| - 1) - 2) + 3)/(1(-1(3|x - 2| - 1) - 2) + 3), g(x) = -1((2x - 2)/(-1x + 3))^2 + 3((2x - 2)/(-1x + 3)) - 3, x = 1.7, 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3cos(3\u03c0(-1(-1|x - 3| + 2) - 1) - 1) - 3)^2 - 4 and g(x) = 3((-1(2|x - 3|) + 3)/(2(2|x - 3|) + 2)) - 2 between the vertical lines x = -3.2 and x = -3.0. 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": "Calculate the area enclosed between the functions f(x) = 1sin(1\u03c0(-1|(5x - 4) + 1| + 1) - 3) - 1 and g(x) = -2|(-3x - 4) - 2| - 1 from x = -2.0 to x = -1.9. 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) = (1(3(-3sin(1\u03c0x - 1) + 3)^2 - 5(-3sin(1\u03c0x - 1) + 3) + 5) + 3)/(-2(3(-3sin(1\u03c0x - 1) + 3)^2 - 5(-3sin(1\u03c0x - 1) + 3) + 5)) and g(x) = 3cos(1\u03c0((-3x + 2)/(2x + 1)) + 2) - 3 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": "Determine the area of the region enclosed by the graphs of f(x) = -1|(3(-3x - 4)^2 + 1(-3x - 4) + 2) - 1| + 2 and g(x) = 3cos(1\u03c0((-1x - 3)/(1x + 1))) - 1 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": "Find the area of the region bounded by the curves f(x) = (3(5(2e^(-2x) - 1)^2 - 1(2e^(-2x) - 1) - 3) - 3)/(1(5(2e^(-2x) - 1)^2 - 1(2e^(-2x) - 1) - 3)), g(x) = -2|(5x^2 + 3x - 5) + 1| + 3, x = 0.0, 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": "11.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3cos(2\u03c0(-1(-3|x + 3| - 1)^2 + 1(-3|x + 3| - 1) + 5) - 2) - 1) - 1)/(-1(-3cos(2\u03c0(-1(-3|x + 3| - 1)^2 + 1(-3|x + 3| - 1) + 5) - 2) - 1) - 1) and g(x) = -3|(1(1x - 5)^2 - 1(1x - 5)) + 3| + 2 between the vertical lines x = 3.9 and x = 4.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = -1(-4((3x - 1)/(2x))^2 + 2((3x - 1)/(2x)) + 1) - 2 and g(x) = -2(-1sin(2\u03c0x + 1) - 2)^2 - 4(-1sin(2\u03c0x + 1) - 2) + 5 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": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(2(-5x + 4)^2 - 5) + 2| - 1 and g(x) = 5(-2|x + 3| + 2) + 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": "25.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((1(3cos(2\u03c0x) - 1) + 3)/(3(3cos(2\u03c0x) - 1))) + 3 and g(x) = -1|(1x^2 - 2x + 2) - 1| + 3 between the vertical lines x = -2.2 and x = -1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3sin(1\u03c0((-3(-1x^2 + 3x + 3) + 3)/(-2(-1x^2 + 3x + 3) + 3)) - 2) + 2) - 2 and g(x) = 2(-5(2|x| - 2) - 4)^2 + 1 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1\u03c0(-2((-2(1|x - 3| + 2) + 3)/(-2(1|x - 3| + 2) - 2))^2 + 5((-2(1|x - 3| + 2) + 3)/(-2(1|x - 3| + 2) - 2)) + 4)) + 1 and g(x) = 1(-2cos(2\u03c0((-1x - 1)/(1x - 3)) + 3) - 1)^2 + 1 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": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(2sin(2\u03c0x - 3) + 1) - 2|) + 5 and g(x) = (-1(-2x) - 3)/(-3(-2x) + 2) 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-3(-2x + 3)^2 - 2(-2x + 3) + 2) - 1| - 3) - 3)/(1(-2|(-3(-2x + 3)^2 - 2(-2x + 3) + 2) - 1| - 3)) and g(x) = -1cos(1\u03c0((3(1x - 3) + 1)/(1(1x - 3) + 1)) + 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3(-1(-3|x + 2| - 3)^2 + 3(-3|x + 2| - 3) + 2) - 5) - 3)/(2(-3(-1(-3|x + 2| - 3)^2 + 3(-3|x + 2| - 3) + 2) - 5) - 1) and g(x) = 1cos(2\u03c0(-1(-2x^2 - 4) + 5)) - 2 from x = -4.9 to 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(1(2|x + 1| + 2)^2 - 2(2|x + 1| + 2)) - 3)/(-1(1(2|x + 1| + 2)^2 - 2(2|x + 1| + 2)) + 3) and g(x) = -1(-1x^2 - 1x - 3) - 4 between the vertical lines x = -1.0 and x = 0.0. 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) = -1(-1e^(2(-2|(5x + 3) + 3| + 3)) + 1)^2 + 3, g(x) = 1((-3(-2x^2 - 3x + 4) + 1)/(2(-2x^2 - 3x + 4) + 2)), x = -1.0, 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": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-2|(3sin(2\u03c0(-1x^2 + 5x + 5) - 1) - 3) + 2| - 1) - 2, g(x) = (-3(3|(-2sin(1\u03c0x + 3) + 3) - 1| - 3) + 3)/(2(3|(-2sin(1\u03c0x + 3) + 3) - 1| - 3) - 1), x = -4.8, 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": "67.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(1(-1|x - 1| + 1) - 2) - 1) and g(x) = 1(-5x^2 + 3x + 3) + 3 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": "10.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1sin(2\u03c0(-2(5x + 3)^2 - 4)) - 2 and g(x) = (1(-4x^2 - 3x + 1) + 3)/(-3(-4x^2 - 3x + 1) + 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((-2(5x^2 - 1x + 5))/(-2(5x^2 - 1x + 5) + 3)) - 3 and g(x) = 2|(3e^(-2x) + 1) - 2| + 2 from x = 0.2 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((-1(-3x^2 + 5x + 4) + 2)/(1(-3x^2 + 5x + 4) + 1)) + 3, g(x) = 1(-5x + 4)^2 - 4, x = 0.3, 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": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(1((3(-3|x + 2| + 1))/(-2(-3|x + 2| + 1) + 3))^2 + 3) - 5 and g(x) = (1(5(-1x + 3)^2 + 2))/(1(5(-1x + 3)^2 + 2) - 3) 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": "20.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(1sin(1\u03c0(3(-2|x - 2|)^2 + 5(-2|x - 2|) + 3) + 2) - 3) and g(x) = 1(-2cos(3\u03c0(-4x) - 3) + 3)^2 - 1 from x = -2.5 to x = -2.4. 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(1(5(2cos(3\u03c0x - 1) - 1))^2 - 2(5(2cos(3\u03c0x - 1) - 1)) + 2) + 1)/(1(1(5(2cos(3\u03c0x - 1) - 1))^2 - 2(5(2cos(3\u03c0x - 1) - 1)) + 2) + 3), g(x) = (1(3cos(3\u03c0(3|x + 2| - 1) + 1) + 1) - 1)/(-1(3cos(3\u03c0(3|x + 2| - 1) + 1) + 1) + 2), x = 2.7, 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": "Calculate the area enclosed between the functions f(x) = (-2(3(2(-3|x + 1| - 3) - 5)^2 - 3(2(-3|x + 1| - 3) - 5) - 5) - 2)/(2(3(2(-3|x + 1| - 3) - 5)^2 - 3(2(-3|x + 1| - 3) - 5) - 5) - 1) and g(x) = 2((-2(3cos(1\u03c0x - 2) - 1) - 3)/(1(3cos(1\u03c0x - 2) - 1))) from x = 2.0 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-3(-1x - 3) - 2)/(-1(-1x - 3) + 3)) - 2| and g(x) = -3cos(2\u03c0(-1|x - 1| - 1) - 1) - 1 between the vertical lines x = 1.1 and x = 1.6. 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) = (-2(4(3|(1x - 2) - 1| - 3)^2 - 2(3|(1x - 2) - 1| - 3) - 3) - 1)/(3(4(3|(1x - 2) - 1| - 3)^2 - 2(3|(1x - 2) - 1| - 3) - 3) + 1) and g(x) = (-1(-1(2|x - 1| - 2)^2 + 1(2|x - 1| - 2) + 4) + 3)/(-3(-1(2|x - 1| - 2)^2 + 1(2|x - 1| - 2) + 4) + 1) from x = 0.6 to x = 1.4. 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": "Calculate the area enclosed between the functions f(x) = (-2(5(1(-2|x + 3|) - 4)^2 - 3(1(-2|x + 3|) - 4) + 1) - 2)/(3(5(1(-2|x + 3|) - 4)^2 - 3(1(-2|x + 3|) - 4) + 1) + 1) and g(x) = 3|((1(4x) + 3)/(2(4x) + 3)) + 3| - 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": "26.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-2sin(3\u03c0(3x + 2) - 1) + 2) - 2| - 3 and g(x) = -5(-2sin(1\u03c0x) + 3)^2 + 3(-2sin(1\u03c0x) + 3) + 2 from x = 2.3 to x = 2.7. 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) = 2sin(1\u03c0((-3(-2(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 2) - 2)/(-1(-2(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 2) + 2))) + 3 and g(x) = 2(-3|(-1cos(2\u03c0x) + 2)| + 3)^2 - 2(-3|(-1cos(2\u03c0x) + 2)| + 3) - 3 from x = 1.2 to x = 1.8. 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) = -2cos(2\u03c0(2((-1(1x^2 - 4x + 5))/(1(1x^2 - 4x + 5) + 2)) + 1)) + 1, g(x) = -3|(3((-1x - 2)/(-2x + 3))^2 + 3((-1x - 2)/(-2x + 3)) - 2) - 2| + 2, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(2(-2(2sin(3\u03c0x - 1) - 2) + 2)^2 + 5(-2(2sin(3\u03c0x - 1) - 2) + 2) + 1) - 2)/(-2(2(-2(2sin(3\u03c0x - 1) - 2) + 2)^2 + 5(-2(2sin(3\u03c0x - 1) - 2) + 2) + 1) + 3) and g(x) = -1cos(2\u03c0(-2(1x - 2)^2 + 4(1x - 2) + 2) + 1) + 2 from x = -2.4 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2|(3cos(1\u03c0x - 1) + 1) + 3| - 1)^2 - 1(2|(3cos(1\u03c0x - 1) + 1) + 3| - 1), g(x) = (2(-3x + 5) + 3)/(-1(-3x + 5) + 2), x = 1.1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(3e^(1(5x^2 + 5x + 2)) - 1) + 2)/(1(3e^(1(5x^2 + 5x + 2)) - 1)), g(x) = 3cos(2\u03c0(-2|x - 3| - 1) + 3) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(3\u03c0((3(-2|(3x - 5) + 1| - 1) - 3)/(3(-2|(3x - 5) + 1| - 1))) + 1) + 1 and g(x) = -1((1(1|x - 3| - 1) + 1)/(1(1|x - 3| - 1) + 1))^2 + 1((1(1|x - 3| - 1) + 1)/(1(1|x - 3| - 1) + 1)) between the vertical lines x = 1.4 and x = 2.0. 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) = 2cos(3\u03c0((-3(-1x^2 - 1x - 4) + 2)/(-1(-1x^2 - 1x - 4) - 3)) + 1) + 1 and g(x) = -1((2x + 2)/(-1x - 3)) between the vertical lines x = -0.8 and x = -0.7000000000000001. 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|(4((2x + 2)/(3x - 2)) - 1) + 1| + 2, g(x) = -3sin(1\u03c0(-5x - 5) + 1) - 3, x = -3.3, 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": "Calculate the area enclosed between the functions f(x) = -3(3e^(1(-4(3|x - 2| - 3) + 4)) + 3)^2 - 3(3e^(1(-4(3|x - 2| - 3) + 4)) + 3) + 5 and g(x) = (-1(1|(-1cos(1\u03c0x) + 2) - 1| + 1) - 2)/(-2(1|(-1cos(1\u03c0x) + 2) - 1| + 1) + 3) from x = -1.7 to x = -0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(2sin(3\u03c0((3(2x + 5) - 1)/(1(2x + 5))) + 2) + 3)| and g(x) = -1(-1e^(-1((2x + 2)/(-1x))) + 2) + 1 from x = -2.4 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-1|(-1x^2 + 3x + 4) + 3| + 1) + 3 and g(x) = (-1(-5x - 4) + 2)/(1(-5x - 4)) 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1((-2(-1|x - 1| + 3) + 1)/(-3(-1|x - 1| + 3) - 3))^2 + 4((-2(-1|x - 1| + 3) + 1)/(-3(-1|x - 1| + 3) - 3)) - 1) + 2, g(x) = -3e^(-1(1(1|x + 1| + 1)^2 + 4(1|x + 1| + 1) + 5)), x = 1.5, 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": "17.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(2\u03c0(-1(1|x| + 2)^2 - 1(1|x| + 2) + 2) + 1) and g(x) = -4((2x - 3)/(3x + 3))^2 + 5((2x - 3)/(3x + 3)) - 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": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3\u03c0((2(-1x - 2) + 3)/(2(-1x - 2) + 2)) + 2) + 2 and g(x) = 1e^(-1((1x + 2)/(-2x + 3))) + 1 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": "Calculate the area enclosed between the functions f(x) = -2(1sin(1\u03c0(-3x - 2) + 1) - 1)^2 + 5(1sin(1\u03c0(-3x - 2) + 1) - 1) + 4 and g(x) = -2sin(2\u03c0(-5x^2 + 4x - 4) - 1) + 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": "3.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3cos(1\u03c0(3|(4((-2x + 1)/(2x - 3)) - 2) + 2| - 2) - 2) + 3 and g(x) = (-1(-1e^(-2(4x - 2))))/(2(-1e^(-2(4x - 2))) - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(5(-2|((2x - 2)/(1x - 2)) + 3|) + 2)^2 + 2(5(-2|((2x - 2)/(1x - 2)) + 3|) + 2) + 1 and g(x) = 3|(-1(3x^2 + 4x - 5) - 5) + 2| + 3 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": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-2sin(3\u03c0(-4x^2 + 3x - 4) - 1) + 3) - 2| - 1 and g(x) = (-1(3sin(1\u03c0x + 3) - 2) - 2)/(-1(3sin(1\u03c0x + 3) - 2) + 2) between the vertical lines x = 4.0 and x = 4.1. 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) = -1|(-1((2x - 2)/(3x - 2)) - 1)| + 1 and g(x) = -2((-1x + 2)/(-1x - 2))^2 - 5((-1x + 2)/(-1x - 2)) + 1 between the vertical lines x = -1.0 and x = 3.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1(1cos(3\u03c0(-3x^2 - 3x - 1) - 1) - 3) - 4) - 3)/(2(-1(1cos(3\u03c0(-3x^2 - 3x - 1) - 1) - 3) - 4)) and g(x) = -1((1(3|x|) + 2)/(2(3|x|) + 1)) + 3 from x = 2.5 to x = 2.6. 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": "Find the area of the region bounded by the curves f(x) = -4(2sin(2\u03c0(5x) - 3) + 1)^2 - 2(2sin(2\u03c0(5x) - 3) + 1) + 2, g(x) = 5(1cos(2\u03c0x)), x = -3.5, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(-2(2|(-1((-3x - 3)/(-3x - 2))^2 + 1((-3x - 3)/(-3x - 2)) + 5) - 1| + 1)) + 2 and g(x) = 3|((-2(-3x^2 + 2x + 4) + 1)/(-3(-3x^2 + 2x + 4) - 2)) + 3| + 1 from x = -0.9 to x = 1.6. 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": "Calculate the area enclosed between the functions f(x) = 4(3(1|x + 2| - 3)^2 + 4(1|x + 2| - 3) - 4) - 1 and g(x) = 2|(-2x^2 - 5x + 4) - 1| + 1 from x = -1.4 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1sin(2\u03c0(-5(1x - 2)^2 + 3(1x - 2) - 4) + 2), g(x) = 1(-1x^2 - 1) + 5, x = -2.0, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1|(-5x^2 + 4x - 2)|) - 5, g(x) = -2(-2cos(3\u03c0x - 3)) - 5, x = 0.4, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(5(1x + 3)^2 + 1(1x + 3) - 3) - 1)/(-1(5(1x + 3)^2 + 1(1x + 3) - 3) + 2) and g(x) = -1(2x + 4)^2 - 2(2x + 4) + 2 between the vertical lines x = -4.1 and x = -3.3. 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": "Find the area of the region bounded by the curves f(x) = -1((3(-1|(-1x + 5) + 1| + 2) + 1)/(3(-1|(-1x + 5) + 1| + 2) + 3))^2 + 2((3(-1|(-1x + 5) + 1| + 2) + 1)/(3(-1|(-1x + 5) + 1| + 2) + 3)) + 1, g(x) = -5(3(1e^(-1x) + 2) + 1)^2 + 2(3(1e^(-1x) + 2) + 1) - 3, x = 3.0, 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": "-12.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(2|(3x^2 - 3x - 1)| - 3) + 1, g(x) = -3(-3cos(2\u03c0x - 1) - 1)^2 - 3(-3cos(2\u03c0x - 1) - 1) - 2, x = -0.1, 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": "25.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3\u03c0((2(-3|(-5x - 1)| + 3))/(-2(-3|(-5x - 1)| + 3) - 1))) - 1 and g(x) = -5(1|((-1x)/(-3x + 1)) - 3| - 2)^2 - 5(1|((-1x)/(-3x + 1)) - 3| - 2) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(3(1sin(1\u03c0x - 3) - 1) - 3) - 2)/(1(3(1sin(1\u03c0x - 3) - 1) - 3) - 3) and g(x) = -2cos(2\u03c0(-5x^2 + 4x - 5) - 3) - 3 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(-4(-2cos(1\u03c0x - 3) - 1)^2 - 3(-2cos(1\u03c0x - 3) - 1) - 4) - 3, g(x) = -5(1cos(1\u03c0x - 1) + 3)^2 - 4(1cos(1\u03c0x - 1) + 3) - 5, x = 3.4, 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": "53.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-5((-2(2sin(1\u03c0x + 1)) + 3)/(3(2sin(1\u03c0x + 1)) - 1))^2 + 5((-2(2sin(1\u03c0x + 1)) + 3)/(3(2sin(1\u03c0x + 1)) - 1)) + 1) - 2, g(x) = (-2(3e^(-2(3x^2 - 4x + 5)) - 1) + 3)/(-2(3e^(-2(3x^2 - 4x + 5)) - 1) + 1), x = -0.2, 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": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(-3x - 5) - 2)/(-3(-3x - 5) + 1))^2 - 1((-2(-3x - 5) - 2)/(-3(-3x - 5) + 1)) - 1 and g(x) = (3(-5x + 5) - 1)/(-3(-5x + 5) - 1) between the vertical lines x = -1.4 and 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": "Calculate the area enclosed between the functions f(x) = (3(-3|(2cos(3\u03c0x - 1) + 3) - 2| + 1))/(2(-3|(2cos(3\u03c0x - 1) + 3) - 2| + 1) - 1) and g(x) = -2e^(-1((3x + 1)/(1x - 3))) - 2 from x = -4.8 to x = -4.7. 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) = (-1(2(5(3|x + 1| - 1) + 5)^2 - 1(5(3|x + 1| - 1) + 5) - 2) - 1)/(-2(2(5(3|x + 1| - 1) + 5)^2 - 1(5(3|x + 1| - 1) + 5) - 2) + 3) and g(x) = -4((-2(3sin(2\u03c0x - 2) - 3) + 2)/(-3(3sin(2\u03c0x - 2) - 3) + 4)) - 3 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(2|(1((2x - 1)/(2x + 2))^2) - 1| + 1) - 1 and g(x) = (2(-2|(2e^(2x) - 3) - 2| + 2) + 2)/(-1(-2|(2e^(2x) - 3) - 2| + 2) - 2) 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": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(3(1|x| - 2) + 2)^2 - 2(3(1|x| - 2) + 2) - 3) + 1)/(2(-1(3(1|x| - 2) + 2)^2 - 2(3(1|x| - 2) + 2) - 3) - 1), g(x) = -3cos(1\u03c0((-1(-3x - 2) + 3)/(-1(-3x - 2))) + 1) - 3, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2|((-1(-3x^2 - 5x + 1) + 2)/(-1(-3x^2 - 5x + 1) - 1)) + 1| + 3) + 3, g(x) = -3|((1(5x^2 + 5x - 3) - 3)/(-1(5x^2 + 5x - 3) - 1)) - 1| + 1, x = -1.4, 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": "24.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(2sin(2\u03c0(-2(3x + 3)^2 + 3(3x + 3) + 1) + 1) + 2) - 1)/(-3(2sin(2\u03c0(-2(3x + 3)^2 + 3(3x + 3) + 1) + 1) + 2) + 2) and g(x) = 1(1|((-2x)/(-3x + 1)) + 3| - 1)^2 - 5(1|((-2x)/(-3x + 1)) + 3| - 1) - 1 from x = -1.4 to x = -1.2999999999999998. 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) = (1(2(3|(1x + 2) - 3| + 2)^2 - 2(3|(1x + 2) - 3| + 2) - 5) - 1)/(2(2(3|(1x + 2) - 3| + 2)^2 - 2(3|(1x + 2) - 3| + 2) - 5) - 1), g(x) = -1(1e^(-1(-3|x - 2| + 3)) - 1)^2 + 1(1e^(-1(-3|x - 2| + 3)) - 1) - 4, x = 0.9, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-5(2|(3x^2 + 4x + 3) + 1| - 3) + 4) - 3)/(3(-5(2|(3x^2 + 4x + 3) + 1| - 3) + 4) + 1) and g(x) = -1e^(-2(-1|((2x + 2)/(2x + 3)) - 2|)) + 3 from x = -3.1 to x = -1.8. 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) = -3|((-2(-1x + 5) + 2)/(1(-1x + 5) + 1)) + 1| + 2, g(x) = -1cos(2\u03c0(-1x + 5) + 3) + 1, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(5(-2|((1x - 1)/(2x - 1)) - 1| + 3) + 3)^2 + 5(5(-2|((1x - 1)/(2x - 1)) - 1| + 3) + 3) - 2 and g(x) = -3|(-4(-5x + 2)^2 - 2(-5x + 2)) + 3| + 2 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": "-1069.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5((1(3sin(3\u03c0x - 2) + 3))/(3(3sin(3\u03c0x - 2) + 3) - 1))^2 + 4((1(3sin(3\u03c0x - 2) + 3))/(3(3sin(3\u03c0x - 2) + 3) - 1)) - 3 and g(x) = 1(-3|x - 1| + 1) - 1 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": "42.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(2e^(1(3|(1x^2 - 4x + 4) - 2| - 1)) - 3) + 2)/(-3(2e^(1(3|(1x^2 - 4x + 4) - 2| - 1)) - 3) + 2) and g(x) = (2(-1(-3e^(-1x) - 3)))/(-2(-1(-3e^(-1x) - 3))) 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(3e^(-1((-2(1x - 4) - 2)/(-3(1x - 4) + 4))) + 3) + 1| + 2, g(x) = (3(-3(-2sin(1\u03c0x - 2) - 3) - 4) - 1)/(-2(-3(-2sin(1\u03c0x - 2) - 3) - 4) + 3), x = -2.2, 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": "10.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-2(-5x - 1) - 2)/(3(-5x - 1) + 3)) + 2|, g(x) = -1|(-5x + 4) - 1| + 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": "2.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-1e^(1(5((2x + 1)/(2x))^2 + 3((2x + 1)/(2x)) - 2)) + 3) - 1 and g(x) = -3(-3e^(-2((1x + 2)/(1x + 3))) + 2)^2 + 1(-3e^(-2((1x + 2)/(1x + 3))) + 2) + 3 from x = -2.4 to x = -1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|((-2x - 3)/(1x))| + 1)^2 - 3(-1|((-2x - 3)/(1x))| + 1) + 4 and g(x) = (1(2|x|) - 1)/(-2(2|x|) + 3) 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": "9.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-3(2x - 3) - 3)/(1(2x - 3) + 2))^2 and g(x) = (2(3sin(1\u03c0x - 1) - 1) - 1)/(3(3sin(1\u03c0x - 1) - 1) - 2) from x = 3.1 to x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-2|(-1x - 4)|)^2 + 1(-2|(-1x - 4)|) - 1, g(x) = -2sin(3\u03c0(1x - 3) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(5(-2cos(3\u03c0x + 2) - 3) + 4))/(-3(5(-2cos(3\u03c0x + 2) - 3) + 4) - 1), g(x) = (2(3cos(3\u03c0x + 1) - 1) + 3)/(2(3cos(3\u03c0x + 1) - 1) + 1), x = -4.3, 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3(2|x| + 2) + 3)/(3(2|x| + 2) - 1)) - 1 and g(x) = 1|(-3cos(2\u03c0x - 1) + 1) - 1| - 2 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3((1(1|(-1x - 1) + 3| + 1) - 3)/(2(1|(-1x - 1) + 3| + 1) + 3))^2 + 3((1(1|(-1x - 1) + 3| + 1) - 3)/(2(1|(-1x - 1) + 3| + 1) + 3)) - 2 and g(x) = (-3(2(-1x^2 - 5x) + 5) - 1)/(2(2(-1x^2 - 5x) + 5) + 1) 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((2(2|x + 3| - 1) + 1)/(3(2|x + 3| - 1) - 1)) - 4 and g(x) = -5(2x - 5)^2 + 3 between the vertical lines x = 2.0 and x = 3.0. 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) = -3|(-2(-5x^2 + 4x + 4) - 2) - 1| - 3 and g(x) = (-3(-3cos(3\u03c0x - 3) + 3) - 1)/(-1(-3cos(3\u03c0x - 3) + 3) + 2) 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": "86.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(1(-2|(1sin(3\u03c0x - 2) + 2) + 2| + 1) + 4) - 2)/(2(1(-2|(1sin(3\u03c0x - 2) + 2) + 2| + 1) + 4) - 1), g(x) = (1(-2|(-2cos(2\u03c0x + 2) - 3) + 2| + 2) - 3)/(-3(-2|(-2cos(2\u03c0x + 2) - 3) + 2| + 2) + 2), 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((2(-4x - 4) + 2)/(2(-4x - 4) - 1))^2 - 4((2(-4x - 4) + 2)/(2(-4x - 4) - 1)) - 4, g(x) = -2sin(3\u03c0(3x^2 + 2x + 3) + 1) - 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": "Calculate the area enclosed between the functions f(x) = 2|(1(2sin(3\u03c0x + 3))^2 + 3(2sin(3\u03c0x + 3)) + 3)| - 2 and g(x) = 4(2sin(2\u03c0x - 2) + 1)^2 + 5(2sin(2\u03c0x - 2) + 1) + 5 from x = -4.7 to x = -4.2. 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) = (-2(-1|(-4(-5x - 1)^2 - 5(-5x - 1) - 2) + 3| - 1))/(2(-1|(-4(-5x - 1)^2 - 5(-5x - 1) - 2) + 3| - 1) - 3) and g(x) = (3(-1(3|x + 3| - 2)^2 + 5) - 2)/(1(-1(3|x + 3| - 2)^2 + 5) + 1) from x = -4.4 to x = -1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0(3|((1x + 3)/(-1x)) + 1| + 1) - 1) - 2 and g(x) = -2cos(2\u03c0(-2|x + 3| + 1) - 3) - 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": "Calculate the area enclosed between the functions f(x) = -1(-2sin(3\u03c0(-2x^2 + 3x + 3)) + 2) + 3 and g(x) = 2sin(2\u03c0(-2x - 1) - 2) - 2 from x = -4.3 to x = -4.2. 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) = 2sin(2\u03c0(-3|((2x - 2)/(-3x)) + 1| + 1) + 2) - 3, g(x) = (2(-2cos(3\u03c0x) - 2))/(-2(-2cos(3\u03c0x) - 2) - 3), 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": "5.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2((3(5(2|x - 1| + 2)^2 - 1(2|x - 1| + 2) - 3) - 2)/(-1(5(2|x - 1| + 2)^2 - 1(2|x - 1| + 2) - 3) - 1)) + 1, g(x) = -1((2(4x^2 + 5x - 5) - 2)/(-3(4x^2 + 5x - 5) + 4)) + 2, x = -2.0, 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": "12.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(4(-1cos(1\u03c0(4x^2 + 5x + 2) + 2)) + 2) + 2| + 1 and g(x) = 3((-3(2cos(1\u03c0x - 2) - 3) - 3)/(3(2cos(1\u03c0x - 2) - 3) - 1)) - 3 between the vertical lines x = -3.8 and x = -3.6999999999999997. 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(-1|((2x + 2)/(3x))| - 1)^2 + 3(-1|((2x + 2)/(3x))| - 1) - 2 and g(x) = -3((-1x + 2)/(2x + 3))^2 + 2((-1x + 2)/(2x + 3)) - 2 between the vertical lines x = -2.9 and x = -0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-31.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(1|(-1e^(-1(1x + 2)))| + 3)^2 - 2(1|(-1e^(-1(1x + 2)))| + 3) - 2 and g(x) = -1(-3|(-5x - 1) + 1| + 3)^2 - 1(-3|(-5x - 1) + 1| + 3) - 5 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": "57.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-1(-1|(-4x^2 - 1x + 5) + 2| + 1) - 1)/(-1(-1|(-4x^2 - 1x + 5) + 2| + 1) - 2)) - 2 and g(x) = (1(1e^(-1(2x^2 + 3x - 2)) + 2) - 2)/(-3(1e^(-1(2x^2 + 3x - 2)) + 2) + 2) from x = -0.9 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": "Determine the area of the region enclosed by the graphs of f(x) = 2((3(1sin(1\u03c0x + 1) - 2) - 2)/(-3(1sin(1\u03c0x + 1) - 2) + 1))^2 + 3((3(1sin(1\u03c0x + 1) - 2) - 2)/(-3(1sin(1\u03c0x + 1) - 2) + 1)) - 1 and g(x) = -1(4x^2 - 5x - 3) - 3 between the vertical lines x = -0.3 and x = 1.6. 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) = 4(4(-3cos(3\u03c0((-2x - 3)/(2x - 3)) + 1)) + 1)^2 - 2(4(-3cos(3\u03c0((-2x - 3)/(2x - 3)) + 1)) + 1) + 4 and g(x) = 3|((3(1x - 4))/(-3(1x - 4) - 1)) + 1| - 3 from x = 3.7 to x = 3.8000000000000003. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(5(-1(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 2) - 2) - 3)/(-2(5(-1(-1|x + 2| + 2)^2 + 4(-1|x + 2| + 2) + 2) - 2)) and g(x) = 1|(-5((2x + 2)/(3x)) + 1) + 3| + 1 from x = -4.3 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2(-2(4x - 4)^2 - 4(4x - 4) + 5) + 3)/(3(-2(4x - 4)^2 - 4(4x - 4) + 5))) - 3| - 2 and g(x) = -1|(-4(-1x - 3)^2 - 1(-1x - 3) - 1) - 2| - 1 between the vertical lines x = -2.6 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1sin(2\u03c0(5(-3|(-3x - 1) - 1| - 3)^2) + 2) and g(x) = -3cos(2\u03c0(-1(-3x^2 + 3x)) + 3) + 1 between the vertical lines x = 1.8 and x = 1.9000000000000001. 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(3(-5(1|x + 2| + 3)^2 + 4) + 2) - 2)/(3(3(-5(1|x + 2| + 3)^2 + 4) + 2) - 2), g(x) = (3(-1(-2|x - 2|)^2 + 4(-2|x - 2|) + 1) + 1)/(-3(-1(-2|x - 2|)^2 + 4(-2|x - 2|) + 1) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3(3|x - 1| - 3) + 2)^2 - 2(-3(3|x - 1| - 3) + 2) + 4, g(x) = -3(-1x^2 + 2x - 4) + 4, 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": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-2(2sin(1\u03c0(2|x + 2| + 1) + 2) + 3) + 1)/(3(2sin(1\u03c0(2|x + 2| + 1) + 2) + 3) + 1)) + 1 and g(x) = 4((2(-3|x| + 3))/(-3(-3|x| + 3) + 1)) + 4 between the vertical lines x = 2.3 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2|(-3sin(3\u03c0x + 1) + 2) - 1| + 3) - 3)/(-1(-2|(-3sin(3\u03c0x + 1) + 2) - 1| + 3)) and g(x) = 3cos(3\u03c0(-1x^2 - 5x - 4) + 3) - 2 between the vertical lines x = 2.4 and 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": "Calculate the area enclosed between the functions f(x) = 2(-2sin(3\u03c0((-1x + 3)/(1x + 3))) + 3) + 4 and g(x) = 1(5x^2 + 5x - 3) - 1 from x = -2.4 to x = -2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-3(1x^2 + 5x + 2) + 1)/(2(1x^2 + 5x + 2) - 1)) - 5 and g(x) = -3|(1x + 5) - 1| - 1 between the vertical lines x = -3.2 and x = -0.3. 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) = 3|((-1(1x + 5) + 3)/(1(1x + 5) - 2)) + 3| + 2, g(x) = 1(-2e^(1x) + 1) + 2, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2sin(3\u03c0(-5x + 5) - 1) - 3) - 3|, g(x) = 2e^(2(-3x + 5)) + 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": "Determine the area of the region enclosed by the graphs of f(x) = -1|(5(-3x^2 + 3x - 1) - 4) + 2| + 2 and g(x) = 2(-2|x + 3| + 3) - 2 between the vertical lines x = -0.1 and x = 1.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1(-1x - 3)^2 - 3(-1x - 3) - 5))/(-2(1(-1x - 3)^2 - 3(-1x - 3) - 5) - 3) and g(x) = 1sin(2\u03c0((-2x + 2)/(-2x - 1)) + 2) + 2 between the vertical lines x = -3.1 and 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": "Calculate the area enclosed between the functions f(x) = 2(-2cos(2\u03c0(3|x - 1| - 3)) + 1)^2 - 2(-2cos(2\u03c0(3|x - 1| - 3)) + 1) + 2 and g(x) = 2(1x + 2)^2 - 4 from x = -4.0 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": "Find the area of the region bounded by the curves f(x) = 3(3cos(2\u03c0(3(-3|x - 1| + 2) + 2) - 1))^2 + 1, g(x) = -2sin(2\u03c0(-1|((3x)/(-1x - 1)) - 3| - 2) - 2), 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(-3|(4x + 3) + 1| + 3) - 1)/(2(-3|(4x + 3) + 1| + 3) + 2))^2 - 1((1(-3|(4x + 3) + 1| + 3) - 1)/(2(-3|(4x + 3) + 1| + 3) + 2)) - 5 and g(x) = (-3(-5(3cos(3\u03c0x - 1) + 1) - 4) + 3)/(-3(-5(3cos(3\u03c0x - 1) + 1) - 4)) between the vertical lines x = -2.8 and x = -2.3. 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) = -1(-2cos(1\u03c0(2|(-1x^2 + 3x + 5) - 1| - 3) + 2) - 2) - 1, g(x) = -2|(1((-2x + 2)/(2x))^2 + 3((-2x + 2)/(2x)) + 5) - 3| + 1, x = -4.7, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1|(-2cos(2\u03c0x + 2) + 3) - 1| - 3) + 3)/(1(1|(-2cos(2\u03c0x + 2) + 3) - 1| - 3) + 2) and g(x) = 3|(-2x - 1) - 3| - 2 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": "35.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-5(5x + 5)^2 + 3(5x + 5) - 4) - 1)/(-2(-5(5x + 5)^2 + 3(5x + 5) - 4) - 3) and g(x) = (2(5x^2 - 5x + 4) - 2)/(-3(5x^2 - 5x + 4) + 2) between the vertical lines x = -1.2 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) = 1|((-1(1x - 4) + 1)/(2(1x - 4) - 1)) + 1| - 2, g(x) = 2cos(2\u03c0(-5x^2 + 2x - 2) + 2) + 3, x = 4.4, 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1(-3sin(1\u03c0x + 3) + 1)^2 - 5(-3sin(1\u03c0x + 3) + 1) + 2) - 1)/(-1(-1(-3sin(1\u03c0x + 3) + 1)^2 - 5(-3sin(1\u03c0x + 3) + 1) + 2) - 3), g(x) = 3e^(-2(1x^2 - 5x + 4)) + 1, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(1\u03c0(5(1x^2 - 3) + 2) + 3) + 2 and g(x) = -2|(-5x^2 + 4x - 2) + 2| + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2|(3x^2 - 4x - 1) - 2| + 2) and g(x) = -3((2x)/(-3x - 2))^2 + 1((2x)/(-3x - 2)) - 3 between the vertical lines x = 1.8 and 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": "Calculate the area enclosed between the functions f(x) = 3cos(1\u03c0(-3|((1(-3x^2 + 2) + 3)/(-3(-3x^2 + 2) + 1)) - 1| - 2) - 3) + 2 and g(x) = -1|(1(-1x^2 - 1x - 2) + 4) + 2| + 2 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3|(-3((3x - 3)/(3x + 3))^2 + 3) - 2| + 1) - 1 and g(x) = (3(-4(-3x^2 - 1) + 5))/(1(-4(-3x^2 - 1) + 5) - 2) from x = 0.2 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": "Find the area of the region bounded by the curves f(x) = -1|(1cos(2\u03c0(3(4x^2 + 5x - 4) + 5) - 1) - 2) - 2| + 2, g(x) = -2cos(1\u03c0(5((-2x - 3)/(1x)) - 2) - 2) - 3, x = 0.1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1(2|((2x + 3)/(1x + 2)) + 3|) + 2)^2 + 1(-1(2|((2x + 3)/(1x + 2)) + 3|) + 2) - 2 and g(x) = -1((3(-2sin(2\u03c0x + 3) + 1) + 2)/(-3(-2sin(2\u03c0x + 3) + 1) + 2))^2 + 2((3(-2sin(2\u03c0x + 3) + 1) + 2)/(-3(-2sin(2\u03c0x + 3) + 1) + 2)) + 5 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1|(-3x^2 + 1) - 1| + 2) + 3)/(-3(-1|(-3x^2 + 1) - 1| + 2) - 1) and g(x) = 2sin(3\u03c0(-5x - 4) - 1) - 3 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(3(2sin(2\u03c0(-1|x - 2| - 3) - 2) + 3) + 3) - 3)/(-2(3(2sin(2\u03c0(-1|x - 2| - 3) - 2) + 3) + 3) + 3), g(x) = 1sin(3\u03c0(1(2x + 5)^2 - 2(2x + 5) + 1) - 3) + 1, x = 2.5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1sin(1\u03c0((2x - 3)/(1x - 3)) + 1))^2 - 5 and g(x) = -5(-4x - 1)^2 - 2(-4x - 1) - 2 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(5(-2e^(1x) + 2) - 3)|, g(x) = -3|(1x^2 - 3x - 2) - 2| - 2, x = -0.9, 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": "14.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(4(3cos(3\u03c0(-1x^2 - 5x - 5) - 1) + 3) - 2) + 1)/(3(4(3cos(3\u03c0(-1x^2 - 5x - 5) - 1) + 3) - 2)) and g(x) = 1cos(1\u03c0(-2((1x - 3)/(3x)) - 5) - 1) - 3 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-1|(-3sin(1\u03c0x + 1))| + 1))/(3(-1|(-3sin(1\u03c0x + 1))| + 1) - 1), g(x) = 3e^(-2(-1|x - 2|)) + 2, x = 1.6, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(1cos(1\u03c0((-3x + 1)/(1x + 1)) + 3)) - 4, g(x) = 1e^(1(1x^2 + 1x - 4)), x = -0.4, and x = -0.30000000000000004. 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) = -3|(1cos(3\u03c0(-5(-1x + 4)^2 - 1) - 3) - 2) - 3| - 2 and g(x) = -3|(-4(3x)^2 - 5)| 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-3cos(1\u03c0(-3|(4x - 3)| + 3) - 3) - 1) + 3)/(-1(-3cos(1\u03c0(-3|(4x - 3)| + 3) - 3) - 1)) and g(x) = (2(3(3|x + 1| - 1) - 3) + 2)/(-2(3(3|x + 1| - 1) - 3) - 1) between the vertical lines x = -0.1 and x = 0.1. 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": "Find the area of the region bounded by the curves f(x) = -5((-3(5x^2 - 3x - 1) - 3)/(1(5x^2 - 3x - 1) + 3)) - 5, g(x) = 5(-1|x + 1|), 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(1\u03c0((2(-4x^2 - 3x + 4) + 1)/(2(-4x^2 - 3x + 4) - 1)) + 2) - 2, g(x) = 1|(3x^2 + 5x - 2) + 1| - 1, x = 0.0, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3(-2|(-2cos(3\u03c0x - 1) + 2) - 1| + 3) + 5)^2 + 4(-3(-2|(-2cos(3\u03c0x - 1) + 2) - 1| + 3) + 5) - 1 and g(x) = (1(1(-2x + 1)^2 + 3(-2x + 1) - 3))/(-2(1(-2x + 1)^2 + 3(-2x + 1) - 3) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(1|(-3(2cos(3\u03c0x + 2) + 3) + 5) + 2|)^2 + 5(1|(-3(2cos(3\u03c0x + 2) + 3) + 5) + 2|) - 4 and g(x) = -3sin(3\u03c0(-5((-2x + 2)/(-1x + 2))^2 - 2((-2x + 2)/(-1x + 2)) - 2) + 2) - 2 from x = 1.6 to x = 1.7000000000000002. 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(3x^2 + 5x - 3) - 2)/(-1(3x^2 + 5x - 3) - 2)) - 2| - 3 and g(x) = 2(3x - 5)^2 - 4(3x - 5) - 2 between the vertical lines x = 0.2 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(2(1x + 5)^2 - 1(1x + 5) - 1))/(3(2(1x + 5)^2 - 1(1x + 5) - 1) + 2) and g(x) = -1(5x + 5)^2 - 3(5x + 5) 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1e^(-1(1x - 2)) - 1) + 1| + 1 and g(x) = -3|((-3x + 1)/(-2x)) - 3| - 2 between the vertical lines x = 0.1 and x = 0.9. 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) = 3|((1(-1(-2cos(1\u03c0x - 1) + 3)^2 + 3(-2cos(1\u03c0x - 1) + 3) + 2) + 1)/(1(-1(-2cos(1\u03c0x - 1) + 3)^2 + 3(-2cos(1\u03c0x - 1) + 3) + 2) + 3)) + 3| - 3 and g(x) = 2|(1((-1x + 1)/(-2x)) - 3) + 2| + 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": "4.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-2(-2|x + 3| + 1) - 1)/(1(-2|x + 3| + 1) - 2))^2 + 2((-2(-2|x + 3| + 1) - 1)/(1(-2|x + 3| + 1) - 2)) and g(x) = 1cos(3\u03c0((2x)/(-3x + 1)) - 3) - 2 from x = -4.9 to x = -3.0. 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) = (3(1(-2cos(3\u03c0x + 2)) - 3) + 2)/(3(1(-2cos(3\u03c0x + 2)) - 3) - 1) and g(x) = 1(-2x^2 + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(2\u03c0(-1|((-3x + 3)/(1x + 1))| - 2) + 3) + 2 and g(x) = -3e^(1((2x - 3)/(1x + 1))) + 1 from x = -0.9 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) = 5(-2|((-3x + 2)/(1x + 1)) + 2| + 3) - 5 and g(x) = -5((1x + 2)/(3x + 1)) + 3 between the vertical lines x = -0.3 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(4((1(3|x + 1| + 1) - 1)/(1(3|x + 1| + 1))) - 3)^2 - 5(4((1(3|x + 1| + 1) - 1)/(1(3|x + 1| + 1))) - 3) - 1 and g(x) = 1cos(3\u03c0(1(-2|x - 2| + 3) + 1) - 3) - 1 from x = -1.0 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": "Find the area of the region bounded by the curves f(x) = -3cos(1\u03c0(-1((-1x)/(-2x + 3))^2 + 2((-1x)/(-2x + 3)) - 1)) + 3, g(x) = (-3(-2x - 3) + 3)/(-3(-2x - 3) + 4), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(2|(5x + 3) - 1| - 1)^2 + 2(2|(5x + 3) - 1| - 1) - 4, g(x) = (-1(-1|x| - 2) + 3)/(-1(-1|x| - 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(2|x + 2| - 3) + 3))/(-2(-1(2|x + 2| - 3) + 3) + 3) and g(x) = 2(-1cos(3\u03c0x - 2) - 3) + 5 between the vertical lines x = -4.9 and x = -4.6. 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) = 3(4((-3x - 2)/(-2x + 3)) + 5)^2 - 2(4((-3x - 2)/(-2x + 3)) + 5) - 4 and g(x) = (1(-1e^(-1x) + 3) + 1)/(-2(-1e^(-1x) + 3) + 1) 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": "41.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3(-3|x + 3| + 2)^2 - 1(-3|x + 3| + 2) + 4) + 3)/(1(-3(-3|x + 3| + 2)^2 - 1(-3|x + 3| + 2) + 4) + 2) and g(x) = -2e^(1(1|x + 1| - 2)) from x = -2.7 to x = -1.8. 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) = -2cos(1\u03c0((3(-1x^2 + 4x + 5) + 2)/(1(-1x^2 + 4x + 5))) + 1) + 1, g(x) = (-2(-1x^2 + 5x + 4) - 3)/(-2(-1x^2 + 5x + 4) + 3), 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) = -1((-2(-1|(1x^2 + 4x - 4) + 3| - 1))/(-2(-1|(1x^2 + 4x - 4) + 3| - 1))) + 1 and g(x) = (3(-4(1|x - 1| - 1) + 1) - 3)/(1(-4(1|x - 1| - 1) + 1) + 3) between the vertical lines x = 0.0 and x = 2.0. 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(-2cos(3\u03c0(2|x + 1| + 2) + 2) + 1) - 1 and g(x) = 3(1x^2 - 4x + 1) - 4 between the vertical lines x = -0.0 and x = 4.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0(5(-2|x - 1|) + 1) + 2) - 3, g(x) = 4(-1|x - 1| + 3)^2 - 5(-1|x - 1| + 3), x = 3.5, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((1(3cos(3\u03c0x - 3) + 3) - 1)/(-2(3cos(3\u03c0x - 3) + 3))) - 1, g(x) = 3|(-1x^2 - 5x - 3) + 2| - 3, x = 4.0, 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": "10.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3(-2(-3|x| + 2)^2 + 2) + 1) - 1)/(3(-3(-2(-3|x| + 2)^2 + 2) + 1) - 2) and g(x) = 3(1|(-5x - 2) + 3| - 2)^2 + 1(1|(-5x - 2) + 3| - 2) - 5 from x = -0.4 to 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": "Calculate the area enclosed between the functions f(x) = 2|(3(-3sin(3\u03c0x + 3) + 1) + 2) - 3| - 1 and g(x) = -3|(1sin(2\u03c0x) - 1) + 2| from x = 1.7 to x = 1.8. 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) = 3sin(3\u03c0(3|(-4x^2 + 1x - 2) - 2| - 2) + 3) and g(x) = -1sin(2\u03c0((3x + 1)/(-2x - 1)) - 2) - 1 from x = -1.3 to x = -1.2. 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) = 2sin(1\u03c0(-1((-2x - 1)/(1x - 2))^2 + 4((-2x - 1)/(1x - 2)) - 3) + 1) - 1 and g(x) = (1(4x^2 - 5x - 5) + 3)/(3(4x^2 - 5x - 5) - 1) from x = 3.3 to x = 3.4. 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) = (3(-1(-2(1|x - 1|) + 3)^2 - 4(-2(1|x - 1|) + 3) - 4) + 2)/(-2(-1(-2(1|x - 1|) + 3)^2 - 4(-2(1|x - 1|) + 3) - 4) + 3), g(x) = (-3(4(-3sin(3\u03c0x - 2) - 1)^2 + 2(-3sin(3\u03c0x - 2) - 1) - 4) + 2)/(-2(4(-3sin(3\u03c0x - 2) - 1)^2 + 2(-3sin(3\u03c0x - 2) - 1) - 4) + 1), 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3|(3x^2 + 5x + 3) - 3| + 1) - 2 and g(x) = -1|(-5x^2 + 3x) - 1| + 1 from x = -1.9 to x = -1.5. 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": "Find the area of the region bounded by the curves f(x) = (-1(-1(-4(2|x + 2| - 1) - 2)^2 - 5(-4(2|x + 2| - 1) - 2) - 3) - 3)/(1(-1(-4(2|x + 2| - 1) - 2)^2 - 5(-4(2|x + 2| - 1) - 2) - 3) + 3), g(x) = -1(2|(5x - 4) + 1| + 3)^2 + 5(2|(5x - 4) + 1| + 3) - 2, 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2(-1|(3x^2 - 4x) + 2| + 2) - 1) - 3)/(-1(2(-1|(3x^2 - 4x) + 2| + 2) - 1) + 3), g(x) = (2(-2(-2sin(2\u03c0x - 3) + 3) + 5) - 2)/(1(-2(-2sin(2\u03c0x - 3) + 3) + 5)), x = 3.5, 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(3\u03c0(2|(-2((2x - 1)/(3x)) - 5) - 2| + 2) - 2) - 2 and g(x) = -1|((1(1x) + 3)/(-1(1x) + 2)) + 3| + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-2(-2(2cos(1\u03c0x + 3) - 2)^2 - 2(2cos(1\u03c0x + 3) - 2) - 4) - 1)/(-2(-2(2cos(1\u03c0x + 3) - 2)^2 - 2(2cos(1\u03c0x + 3) - 2) - 4) - 1)) and g(x) = -3(5((-3x - 3)/(3x + 1))^2 - 2((-3x - 3)/(3x + 1)) - 3) from x = -1.8 to x = -0.7. 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": "Calculate the area enclosed between the functions f(x) = -3|(-1(-1cos(3\u03c0(-1x^2 + 3x) + 2) + 3) - 2) + 1| + 2 and g(x) = 5(-3e^(1(-1x^2 - 2x + 1))) + 5 from x = -2.5 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) = 2((3(-3cos(1\u03c0(2x^2 + 3x + 2) + 2) - 1) - 2)/(-2(-3cos(1\u03c0(2x^2 + 3x + 2) + 2) - 1) - 1)) - 2 and g(x) = 1|(-1cos(2\u03c0(2x) - 3) + 2) + 2| + 3 between the vertical lines x = 3.2 and x = 3.3. 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(-4(2|x + 1| + 1)^2 + 5(2|x + 1| + 1) + 1) - 1 and g(x) = -3|(-2cos(2\u03c0x - 2) - 2) + 3| + 2 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(2cos(2\u03c0(5x + 3) - 2) + 3) + 3)/(1(2cos(2\u03c0(5x + 3) - 2) + 3) - 2) and g(x) = -1(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) - 1 from x = -2.4 to 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": "Find the area of the region bounded by the curves f(x) = -1(-3|((-3x + 3)/(3x + 2)) - 1|) + 2, g(x) = (2(-3cos(2\u03c0x - 1) - 2) + 3)/(1(-3cos(2\u03c0x - 1) - 2)), x = -4.2, 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": "9.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2sin(1\u03c0(3x^2 - 2x + 5)) + 2) - 3|, g(x) = -3|(2sin(2\u03c0x) + 2) - 3| + 3, x = -2.0, 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2(-3x^2 + 2x + 4) + 1) + 2)/(1(2(-3x^2 + 2x + 4) + 1)) and g(x) = -3cos(2\u03c0(3|x + 3|) + 1) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3(3sin(2\u03c0((1x - 1)/(1x + 1)) - 2))^2 + 5(3sin(2\u03c0((1x - 1)/(1x + 1)) - 2)) + 4) and g(x) = 1|(-2(3x^2 + 5x - 5) + 3) - 3| - 1 from x = -0.9 to x = -0.8. 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) = -3cos(1\u03c0(3(-2|(-5x^2 - 4x - 2) - 2| + 2) - 2) + 1) + 2 and g(x) = -1cos(2\u03c0(-1|((-2x - 1)/(-3x - 1)) - 2| + 2) + 3) - 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(1e^(-1(-1(-1|x + 2| + 2) + 4)) + 2) + 2)/(3(1e^(-1(-1(-1|x + 2| + 2) + 4)) + 2) - 2) and g(x) = -2(2cos(2\u03c0(2x + 2)))^2 - 3(2cos(2\u03c0(2x + 2))) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(2sin(2\u03c0(-1|x + 3| - 3) + 1) - 2)^2 - 4(2sin(2\u03c0(-1|x + 3| - 3) + 1) - 2) + 2 and g(x) = -3|(-3e^(1x) + 1) + 2| - 1 from x = -0.3 to x = 0.1. 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) = 1(-2|((2(3x^2 + 4x + 1) - 2)/(3(3x^2 + 4x + 1) + 1))| - 1) - 5 and g(x) = -1|((-1(4x^2 - 3x - 5) - 2)/(1(4x^2 - 3x - 5))) + 1| - 1 between the vertical lines x = -0.8 and x = -0.7000000000000001. 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": "Calculate the area enclosed between the functions f(x) = 4(3((-3(-2|x - 3| + 1) + 1)/(-3(-2|x - 3| + 1) - 3)))^2 + 3 and g(x) = 3|(2sin(1\u03c0(-4x) - 2)) - 1| - 1 from x = 3.4 to x = 3.5. 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) = (-2(4(-3e^(-1(1x^2 + 1x)) + 2) + 3) - 1)/(-1(4(-3e^(-1(1x^2 + 1x)) + 2) + 3) + 3) and g(x) = -1((1(2|x - 2| + 1) - 3)/(-2(2|x - 2| + 1) - 1))^2 + 2((1(2|x - 2| + 1) - 3)/(-2(2|x - 2| + 1) - 1)) + 3 from x = 1.1 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) = (2(-2e^(-2(-3|x| + 3))) + 1)/(-3(-2e^(-2(-3|x| + 3))) + 2) and g(x) = 1cos(3\u03c0(-3x^2 - 2x) - 2) + 1 between the vertical lines x = -0.7 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) = 3(-2cos(3\u03c0(3|x - 2| - 2) + 1) - 3)^2 + 3(-2cos(3\u03c0(3|x - 2| - 2) + 1) - 3) - 3 and g(x) = -1|(-1e^(1x) + 2) - 1| + 2 from x = -5.0 to x = -4.9. 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) = 3((1(-3(1|x + 1|) + 3) + 2)/(-1(-3(1|x + 1|) + 3) - 2))^2 - 3((1(-3(1|x + 1|) + 3) + 2)/(-1(-3(1|x + 1|) + 3) - 2)) - 5 and g(x) = -2cos(1\u03c0(-1(-1|x + 1|) - 4) - 2) + 2 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-4(-3|(5x^2 - 1x - 3) + 1| + 1) - 5) - 2)/(-1(-4(-3|(5x^2 - 1x - 3) + 1| + 1) - 5) + 2), g(x) = 3sin(2\u03c0(-1(-3|x| + 1) - 4)) - 3, x = -4.7, 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(5(-3cos(3\u03c0x + 3) - 1) - 3) - 3| - 1 and g(x) = (3(-2sin(1\u03c0x - 2)) + 3)/(-3(-2sin(1\u03c0x - 2)) - 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": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(-3|(-2cos(1\u03c0(-5x^2 + 5x - 4) + 3) + 3) + 1| - 1) - 2 and g(x) = (2(2cos(1\u03c0(-2x^2 - 2x)) + 3) + 1)/(2(2cos(1\u03c0(-2x^2 - 2x)) + 3) - 3) from x = -3.3 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-2(2|x + 1| - 1))/(-3(2|x + 1| - 1) + 1)) + 1 and g(x) = 4(-2sin(3\u03c0x + 3) + 2) + 3 from x = -1.6 to x = -0.4. 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) = (2(3cos(1\u03c0(3x - 3) - 1) + 2) - 2)/(3(3cos(1\u03c0(3x - 3) - 1) + 2)) and g(x) = -1(-1x^2 - 1x - 4) + 4 from x = -4.5 to x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-4(-5(1sin(1\u03c0x + 2) + 1) + 2)^2 + 4(-5(1sin(1\u03c0x + 2) + 1) + 2) - 3) + 2)/(-2(-4(-5(1sin(1\u03c0x + 2) + 1) + 2)^2 + 4(-5(1sin(1\u03c0x + 2) + 1) + 2) - 3) - 3) and g(x) = 4(3((-1x - 2)/(2x + 3))^2 - 5((-1x - 2)/(2x + 3)) - 1) + 1 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(1(-3|x + 1| + 2)) - 3) + 1)/(-2(-1e^(1(-3|x + 1| + 2)) - 3) + 3), g(x) = 2|(-2cos(1\u03c0x + 2) - 1) - 1| - 2, x = -2.0, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1sin(3\u03c0(-4x^2 - 5x)) + 3) - 1)/(2(-1sin(3\u03c0(-4x^2 - 5x)) + 3) + 1), g(x) = (-2(4x - 4) + 3)/(-1(4x - 4) - 1), x = 1.7, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2((3(3sin(1\u03c0x - 2) - 2))/(1(3sin(1\u03c0x - 2) - 2) - 2))^2 - 2) - 3, g(x) = -2|((-2(1x^2 + 1x + 3) + 1)/(-2(1x^2 + 1x + 3) - 3)) + 2| + 3, 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": "15.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(2\u03c0(-1((-1x + 1)/(-2x - 2)) - 1)) + 2, g(x) = 4(-5x - 1)^2 + 5(-5x - 1) - 3, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(2\u03c0((1(-2|x + 3| + 1) - 1)/(-2(-2|x + 3| + 1) + 3)) - 2) + 2 and g(x) = (1(2|x| - 2) - 2)/(3(2|x| - 2) - 2) between the vertical lines x = -1.0 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((-1(-4x + 4) + 1)/(-1(-4x + 4) + 3))^2 + 5((-1(-4x + 4) + 1)/(-1(-4x + 4) + 3)) - 4, g(x) = -2((-1x + 2)/(-1x + 2))^2 + 2((-1x + 2)/(-1x + 2)) - 4, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|((2(-4x + 3) + 1)/(-2(-4x + 3) + 3)) + 2| and g(x) = (1(3sin(1\u03c0x + 3) - 3) - 1)/(-1(3sin(1\u03c0x + 3) - 3) + 2) from x = -2.0 to x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1(-2cos(2\u03c0x + 3) - 2)^2 + 4(-2cos(2\u03c0x + 3) - 2) - 2) - 2, g(x) = 4(2cos(2\u03c0x + 2) - 3), x = 4.4, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1(2e^(-1x) - 1) - 3)/(2(2e^(-1x) - 1))) + 1| + 3 and g(x) = -1|(-1x^2 - 5x) - 1| - 3 between the vertical lines x = 0.4 and x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2|(-3(-3x + 2)^2 + 4(-3x + 2) - 4) - 3| - 1) + 3)/(2(-2|(-3(-3x + 2)^2 + 4(-3x + 2) - 4) - 3| - 1)) and g(x) = 1sin(2\u03c0((1(-3x + 3) + 2)/(-1(-3x + 3))) - 3) - 2 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(1\u03c0(-1(2|x + 3| + 2)^2 - 5(2|x + 3| + 2) - 4) + 3) + 2, g(x) = -4(1e^(1x) - 1)^2 + 2(1e^(1x) - 1) + 3, x = -0.5, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-2(3|((-2x + 1)/(-3x + 1)) + 1| + 1) + 2)^2 - 5(-2(3|((-2x + 1)/(-3x + 1)) + 1| + 1) + 2) - 4, g(x) = -1((2(-1x) + 3)/(3(-1x) + 1))^2 - 2((2(-1x) + 3)/(3(-1x) + 1)) - 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": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(1(3(1|x - 3|)^2 - 5(1|x - 3|) - 3) - 3) - 3)/(-1(1(3(1|x - 3|)^2 - 5(1|x - 3|) - 3) - 3) - 1) and g(x) = 5(-2|(1x^2 + 3x - 1) + 2| + 1) from x = -2.7 to x = -2.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = 3(-1sin(3\u03c0(3|(-3x) - 1| + 1) + 3) - 2)^2 + 5(-1sin(3\u03c0(3|(-3x) - 1| + 1) + 3) - 2) - 3 and g(x) = -2(-2e^(-1((-3x + 3)/(-1x + 2))) + 1)^2 + 2(-2e^(-1((-3x + 3)/(-1x + 2))) + 1) - 1 between the vertical lines x = 4.3 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": "Determine the area of the region enclosed by the graphs of f(x) = -2((-2(-2|x + 2| - 1) + 3)/(1(-2|x + 2| - 1) - 3)) + 1 and g(x) = -1((3x - 3)/(2x - 3)) + 5 between the vertical lines x = -2.3 and 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) = 3(5(-3sin(2\u03c0(2|x + 3|) + 1) + 2) + 2)^2 - 2(5(-3sin(2\u03c0(2|x + 3|) + 1) + 2) + 2) - 2 and g(x) = (-2(-3|(4x^2 - 1x) + 1| + 1) - 2)/(-2(-3|(4x^2 - 1x) + 1| + 1) + 3) from x = 4.1 to x = 4.199999999999999. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2|(3(-2sin(2\u03c0x + 3) + 2)^2 + 4(-2sin(2\u03c0x + 3) + 2) - 5) + 2|) + 1)/(2(-2|(3(-2sin(2\u03c0x + 3) + 2)^2 + 4(-2sin(2\u03c0x + 3) + 2) - 5) + 2|) + 2) and g(x) = -1(-2(1cos(2\u03c0x + 1) + 1) - 3)^2 + 2(-2(1cos(2\u03c0x + 1) + 1) - 3) + 5 from x = 2.6 to x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-3|(-1cos(3\u03c0x - 2) - 2) - 1| - 1) - 3 and g(x) = 3|(-1e^(2x) + 3) + 2| + 2 from x = 0.7 to 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": "Find the area of the region bounded by the curves f(x) = 1|((-1(1x^2 - 4x - 5))/(-2(1x^2 - 4x - 5) - 1)) + 1| + 3, g(x) = (-1(-3sin(2\u03c0x - 1) - 2) + 2)/(-2(-3sin(2\u03c0x - 1) - 2) - 2), x = -4.9, and x = -4.3. Round your answer 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) = -3e^(2(-3(-1x^2 + 4x + 4) - 4)) + 1, g(x) = 1cos(3\u03c0(-3|x + 2| - 2) + 3) + 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-3|((2(-2x + 1) - 2)/(1(-2x + 1) - 2)) - 1|)^2 - 4(-3|((2(-2x + 1) - 2)/(1(-2x + 1) - 2)) - 1|) - 5 and g(x) = -1(2cos(1\u03c0(-4x - 1) + 2) + 1)^2 + 3(2cos(1\u03c0(-4x - 1) + 2) + 1) + 4 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(2cos(2\u03c0(-5x^2 - 1x - 5) - 2) + 3) - 2)/(-1(2cos(2\u03c0(-5x^2 - 1x - 5) - 2) + 3) - 3) and g(x) = (2(-3x^2 - 5x + 1))/(1(-3x^2 - 5x + 1) - 3) 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-1((-2(-5x - 5) - 2)/(-2(-5x - 5) - 1))^2 - 5((-2(-5x - 5) - 2)/(-2(-5x - 5) - 1)) + 3) + 3| + 1 and g(x) = 1cos(3\u03c0(-2|((-1x - 3)/(3x + 3)) - 3| + 1) + 2) + 2 between the vertical lines x = 0.8 and x = 3.4. 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) = (-3(1|(2x^2 + 1x + 2)| - 3) + 1)/(-1(1|(2x^2 + 1x + 2)| - 3) + 2), g(x) = (2(-1e^(2x) + 2) + 2)/(2(-1e^(2x) + 2) - 3), x = -1.8, 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": "93.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-3(1((-1x + 3)/(-1x + 2))^2 + 1((-1x + 3)/(-1x + 2)) - 2) - 3) - 2| + 3 and g(x) = (2(2(-1|x - 3| - 3) + 5))/(-3(2(-1|x - 3| - 3) + 5) - 3) from x = 2.8 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((2(-5x^2 - 5x - 1) - 3)/(-2(-5x^2 - 5x - 1))) - 4, g(x) = 2|(-3x^2 - 2x + 4)| + 3, 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": "87.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-2(-2|x + 2| + 1) - 1) - 3)/(-3(-2(-2|x + 2| + 1) - 1)) and g(x) = -2sin(3\u03c0(5x + 2) - 1) - 3 between the vertical lines x = -2.7 and x = -1.4. 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(1\u03c0(-1|((-3(1x^2) + 3)/(-1(1x^2) - 3)) + 3| + 2) - 2) + 2, g(x) = 2sin(1\u03c0((-2(5x^2 - 3x - 4) + 3)/(-3(5x^2 - 3x - 4) + 2)) + 3) + 1, x = 1.4, 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": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(-2(-2(-4x + 2)^2 - 4(-4x + 2) + 3)) + 2) - 1)/(3(-1e^(-2(-2(-4x + 2)^2 - 4(-4x + 2) + 3)) + 2) - 2), g(x) = (3(3(3|x - 2| - 1)^2 - 1(3|x - 2| - 1) - 5))/(2(3(3|x - 2| - 1)^2 - 1(3|x - 2| - 1) - 5) - 1), x = 1.2, 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-1((3x + 2)/(2x - 3))^2 - 1((3x + 2)/(2x - 3)) - 3) - 4, g(x) = -2(2cos(2\u03c0x + 3) + 2) - 5, x = -0.5, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-4(-3|((-2x)/(2x - 1)) + 2| + 2)^2 + 2(-3|((-2x)/(2x - 1)) + 2| + 2) + 3) + 1, g(x) = 1|((-1(-1x^2 + 4x + 4) + 3)/(-2(-1x^2 + 4x + 4) + 1)) - 1| + 2, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-4(3e^(1(-1x^2 + 3x - 4)) - 1) - 4) + 3| - 3, g(x) = 2sin(3\u03c0(-3(1x^2 + 4x - 3) + 4) + 1), x = -4.8, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(3sin(2\u03c0((3x)/(-1x + 2)) + 1) - 1)^2 - 2 and g(x) = 2|(-2sin(2\u03c0x + 1) - 3) + 1| - 3 from x = 2.7 to x = 3.6. 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": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(-1((3x - 2)/(3x - 2)) + 3) + 1| + 1)^2 - 4(-3|(-1((3x - 2)/(3x - 2)) + 3) + 1| + 1) + 2 and g(x) = 5(1|((-1x + 1)/(-3x + 2)) + 2| - 3) - 5 between the vertical lines x = 0.7 and x = 0.7999999999999999. 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) = -5(1e^(1((-3x - 2)/(2x + 2))) - 1) - 1, g(x) = -2(-3x)^2 + 3, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2sin(1\u03c0(4(5x^2 + 5) - 2) - 1) + 2 and g(x) = 1|(2sin(3\u03c0x + 2)) - 1| + 2 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": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3(5(-2|x + 3| + 2)^2 + 1(-2|x + 3| + 2)) - 1) - 1)/(2(-3(5(-2|x + 3| + 2)^2 + 1(-2|x + 3| + 2)) - 1) + 1) and g(x) = 2(-4((3x - 1)/(2x + 2)) + 1)^2 - 3(-4((3x - 1)/(2x + 2)) + 1) - 1 between the vertical lines x = 0.3 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": "Determine the area of the region enclosed by the graphs of f(x) = 2|(3(-2x + 2)^2 - 2) + 1| and g(x) = 3(1|x|) - 1 between the vertical lines x = 0.9 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": "Find the area of the region bounded by the curves f(x) = 3|((-2(-1x^2 + 2x + 2))/(-3(-1x^2 + 2x + 2) - 1)) - 3| - 3, g(x) = 1|(1e^(-1x) - 3) - 2| - 1, x = -2.3, 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(3\u03c0(-1|(2x + 2)| - 1) + 1) - 2 and g(x) = -3(3x^2 + 4x - 5) from x = -2.2 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3|((3(1e^(-2x) - 1) - 1)/(2(1e^(-2x) - 1) - 3)) - 2| + 3) - 5 and g(x) = -3|(3(-4x - 3)^2 - 2(-4x - 3) + 3)| - 1 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": "94.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(-1((1x + 3)/(-3x)))^2 + 2(-1((1x + 3)/(-3x))) + 4, g(x) = 5(1x^2 + 3x + 2) - 2, x = -2.7, 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": "9.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(1|(3x - 5) - 3| - 3) + 1)/(-3(1|(3x - 5) - 3| - 3) + 1) and g(x) = 2(-3x - 2)^2 + 3(-3x - 2) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(2|(1x - 1) - 3| - 2)^2 - 1(2|(1x - 1) - 3| - 2), g(x) = 3|(2sin(2\u03c0x - 2) - 2) + 2| - 1, x = 2.8, 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": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(3(-3x + 5)^2 - 2(-3x + 5) + 1) + 1| - 1 and g(x) = (1(1cos(2\u03c0x + 1)) + 3)/(-2(1cos(2\u03c0x + 1)) - 1) 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": "31.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((-3(1|(4x^2 - 2x) - 2| + 2) + 1)/(-1(1|(4x^2 - 2x) - 2| + 2) - 2)) - 4, g(x) = (-2(2e^(-1(-4x^2 - 3x + 1)) - 3))/(-2(2e^(-1(-4x^2 - 3x + 1)) - 3) + 3), x = -1.2, 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": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(1\u03c0(3(3|((3x + 1)/(-1x - 3)) + 3| - 3)^2 - 1(3|((3x + 1)/(-1x - 3)) + 3| - 3))), g(x) = 2sin(1\u03c0((-1(1x + 5) + 1)/(-1(1x + 5) + 3)) - 1) + 2, x = -4.2, and x = -4.1000000000000005. 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(1\u03c0(-3|((1(-2x^2 - 2x + 3) - 1)/(3(-2x^2 - 2x + 3) + 2)) + 3| + 2) + 3) + 1, g(x) = 4(-1|((1x + 1)/(3x - 2))| + 2) - 2, x = 0.3, 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": "45.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1sin(3\u03c0(-2|(-5x^2 + 1x + 2) + 3| + 2) - 2) - 2 and g(x) = 5((2x - 3)/(2x + 1))^2 + 1((2x - 3)/(2x + 1)) - 4 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": "Calculate the area enclosed between the functions f(x) = 1|(-3(5((1x + 1)/(-2x - 3))^2) + 2) - 3| + 2 and g(x) = -4(-2|(-3sin(1\u03c0x - 2) - 3) - 2| + 2) + 5 from x = -2.0 to x = -1.4. 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(-3|(4((2x)/(-2x))^2 + 5((2x)/(-2x)) + 3) + 1| + 3) + 2 and g(x) = 5((-3(3cos(3\u03c0x + 2)) + 2)/(-3(3cos(3\u03c0x + 2)) - 3)) - 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": "19.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(5(2|x - 2| - 3) - 2) - 3)/(-2(5(2|x - 2| - 3) - 2)), g(x) = -5(1|x - 1| - 3)^2 + 2(1|x - 1| - 3) + 2, x = 3.5, 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": "7.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(2(2|(3cos(2\u03c0x - 1) - 1) + 2| - 2) - 3)^2 - 1(2(2|(3cos(2\u03c0x - 1) - 1) + 2| - 2) - 3) + 5 and g(x) = -5(-4(-2|x - 3| + 1)^2 + 4(-2|x - 3| + 1) + 5) - 5 from x = 3.0 to x = 3.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1|(-3e^(1(-2x^2 - 5x + 2))) + 3| - 3) - 2 and g(x) = -3e^(-2(2(1|x| + 2)^2 + 4(1|x| + 2))) between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1e^(-1((1(-3|(1x^2 + 5x + 4) + 2| + 1) + 2)/(3(-3|(1x^2 + 5x + 4) + 2| + 1) + 3))) and g(x) = -1|(-1(2cos(2\u03c0x + 2) - 2)^2 - 1) + 1| + 3 from x = -3.6 to x = -3.1. 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) = -4(3sin(3\u03c0(1|x + 1|) + 3) + 1) - 2, g(x) = -1(-3|x + 3| + 2)^2 + 4(-3|x + 3| + 2) + 4, x = -4.3, 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-1|(3((2x)/(-1x + 3))^2 + 5((2x)/(-1x + 3)) + 1) - 1|) - 4 and g(x) = -2(1sin(1\u03c0(-2|x + 2| + 1) + 2) + 3)^2 + 5(1sin(1\u03c0(-2|x + 2| + 1) + 2) + 3) + 2 from x = -3.7 to x = -3.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = (3(-5(-2cos(2\u03c0x - 2) - 3) + 4) + 2)/(-3(-5(-2cos(2\u03c0x - 2) - 3) + 4)) and g(x) = (-1(-3sin(3\u03c0x - 3) + 1) + 3)/(-3(-3sin(3\u03c0x - 3) + 1) + 1) between the vertical lines x = 2.0 and 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": "Calculate the area enclosed between the functions f(x) = -1((-1(-4(-2|x - 3| + 2) - 5) + 2)/(2(-4(-2|x - 3| + 2) - 5) + 2))^2 - 4((-1(-4(-2|x - 3| + 2) - 5) + 2)/(2(-4(-2|x - 3| + 2) - 5) + 2)) + 1 and g(x) = -1((3(1cos(1\u03c0x - 3) + 2) + 1)/(2(1cos(1\u03c0x - 3) + 2) + 2))^2 - 4((3(1cos(1\u03c0x - 3) + 2) + 1)/(2(1cos(1\u03c0x - 3) + 2) + 2)) - 4 from x = 1.5 to x = 4.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3((1(-1|(2x^2 - 1x + 1) + 3|))/(1(-1|(2x^2 - 1x + 1) + 3|))) + 1, g(x) = 5(3|(4x^2 - 2x - 4)| - 3) + 1, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|(-2x - 4)| - 1)^2 - 3(-3|(-2x - 4)| - 1) + 4 and g(x) = 3cos(1\u03c0(-4x^2 + 1x + 2) + 3) - 1 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": "Find the area of the region bounded by the curves f(x) = 3|((-2(4x^2 - 1x - 4))/(-2(4x^2 - 1x - 4) + 3)) - 1| - 2, g(x) = -5((-1x)/(3x + 1)) + 3, x = -0.2, 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": "6.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(3cos(1\u03c0(-2|((-1x + 2)/(1x + 2))| + 2) - 3) + 3) - 4, g(x) = (-1(1|(2x^2 - 1x - 3) + 3|) - 3)/(2(1|(2x^2 - 1x - 3) + 3|) - 1), 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(3|((-3x - 2)/(3x)) - 1| - 3) + 4, g(x) = (-3(-3x - 2) - 3)/(3(-3x - 2) - 1), 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": "Determine the area of the region enclosed by the graphs of f(x) = 1(2|(-2x^2 - 2x - 4) + 2|) - 2 and g(x) = (3(-5x^2 - 4x) - 3)/(-2(-5x^2 - 4x)) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-2(-2sin(1\u03c0(-1x^2 - 1x - 3)) + 3) + 2)/(1(-2sin(1\u03c0(-1x^2 - 1x - 3)) + 3) + 3)) + 2| + 1 and g(x) = (-3(2(5x - 2)^2 - 1) - 3)/(-2(2(5x - 2)^2 - 1)) between the vertical lines x = 0.3 and x = 0.5. 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) = -2(3((1(3|x - 2| - 2) + 2)/(2(3|x - 2| - 2) + 2)) + 3)^2 - 3(3((1(3|x - 2| - 2) + 2)/(2(3|x - 2| - 2) + 2)) + 3) + 4 and g(x) = -3((1(-3sin(3\u03c0x) - 1))/(-1(-3sin(3\u03c0x) - 1) - 2)) between the vertical lines x = 0.0 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(3cos(1\u03c0(1x + 5) - 2) - 1) + 2| + 2, g(x) = 1|(3cos(1\u03c0x - 1) + 3) - 3|, x = -3.0, 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": "3.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-1(3cos(1\u03c0x - 2)) + 5)^2 and g(x) = (-2(-3cos(3\u03c0x + 2) - 2) - 3)/(3(-3cos(3\u03c0x + 2) - 2) - 2) between the vertical lines x = 2.2 and x = 2.7. 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": "Find the area of the region bounded by the curves f(x) = 5(-1|(1x^2 + 3x - 2) - 2| + 3) - 4, g(x) = -1|(-3e^(-1x) - 3) + 3| - 1, x = 0.4, 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": "7.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-3(-3x^2 + 4x + 5))/(-2(-3x^2 + 4x + 5) - 1)) + 4, g(x) = -3sin(3\u03c0(1|x| - 1) + 1) + 3, 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": "Find the area of the region bounded by the curves f(x) = 2|((-3(-4x^2 + 2x + 4) + 1)/(1(-4x^2 + 2x + 4) + 3))| - 1, g(x) = -1cos(3\u03c0((3x + 3)/(3x + 1)) + 1) + 3, 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) = -1((3(1x^2 + 1x - 2) + 1)/(3(1x^2 + 1x - 2))) - 1, g(x) = -2cos(1\u03c0(1|x - 2| + 2) - 2) - 2, x = 0.8, 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": "5.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((1(1|(-4x - 4) + 1| - 1) - 3)/(-3(1|(-4x - 4) + 1| - 1) + 4))^2 - 5((1(1|(-4x - 4) + 1| - 1) - 3)/(-3(1|(-4x - 4) + 1| - 1) + 4)) + 3 and g(x) = (3(3cos(1\u03c0(3x) + 2)) + 1)/(2(3cos(1\u03c0(3x) + 2)) + 3) from x = 0.7 to 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": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3sin(1\u03c0((1(-5x + 5) + 1)/(2(-5x + 5) + 3)) - 1) + 1)| + 1 and g(x) = (2(-4(-1x)^2 + 2(-1x) + 5) - 2)/(3(-4(-1x)^2 + 2(-1x) + 5) + 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2(-5x - 2)^2 - 4(-5x - 2) + 1) + 2)/(2(2(-5x - 2)^2 - 4(-5x - 2) + 1) - 1), g(x) = (3(2x^2 - 1x - 5) + 3)/(-1(2x^2 - 1x - 5) + 2), x = -0.7, 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) = 2(-3(-3|((-3x)/(-1x - 3)) + 3|)^2 + 1(-3|((-3x)/(-1x - 3)) + 3|)) + 4 and g(x) = -1(-2e^(-1(2|x + 3| - 3)) - 2) - 3 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1|(-2(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 1) - 3| + 1) + 2)/(2(-1|(-2(-1e^(1x) + 3)^2 + 5(-1e^(1x) + 3) - 1) - 3| + 1) + 2) and g(x) = 4(1e^(-1(-2x^2 + 4x - 4)) + 1) - 3 from x = 0.0 to x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|((-1(4(-4x^2 - 3x - 4) - 2) + 3)/(-3(4(-4x^2 - 3x - 4) - 2) + 1)) - 2| + 2, g(x) = (-1(2(-1|x| - 2)^2 + 5(-1|x| - 2)) + 2)/(-2(2(-1|x| - 2)^2 + 5(-1|x| - 2)) + 3), x = -0.8, 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": "4.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((2(2|x + 3| + 1) - 3)/(-3(2|x + 3| + 1) - 3)) - 3, g(x) = -1cos(3\u03c0(1|x + 2| - 3) - 1) - 2, x = -3.2, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(3\u03c0(-4(-2x^2 - 3x - 4) - 5) - 3) + 2 and g(x) = 3sin(1\u03c0(-4x^2 + 2x - 5) - 1) - 3 from x = 1.5 to x = 3.3. 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": "Calculate the area enclosed between the functions f(x) = -2e^(1((-2(1|x + 2| - 1) - 1)/(3(1|x + 2| - 1) + 1))) + 3 and g(x) = -3((1x + 3)/(1x + 3)) + 1 from x = -2.6 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": "Determine the area of the region enclosed by the graphs of f(x) = 3((-3(3|(-1x^2 - 2x - 1) + 3|) - 3)/(2(3|(-1x^2 - 2x - 1) + 3|))) + 4 and g(x) = -2(-1|(-1x - 2) + 2| - 2)^2 - 3(-1|(-1x - 2) + 2| - 2) - 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": "19.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|((2(5x - 2) + 3)/(-3(5x - 2) + 4)) + 3| + 1 and g(x) = 1|(2x + 4) - 3| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-3(1sin(2\u03c0(-2x^2 - 4x - 5) + 1)) - 3) + 2| and g(x) = (-1(-2|(1e^(1x)) + 2|) + 3)/(-1(-2|(1e^(1x)) + 2|) + 2) between the vertical lines x = 4.3 and x = 4.3999999999999995. 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) = 1sin(1\u03c0((2(-2|(2x - 5) + 2| + 3) - 2)/(-3(-2|(2x - 5) + 2| + 3) - 3)) + 3) + 3 and g(x) = (-2(-5(-3|x - 1|) - 5) - 2)/(3(-5(-3|x - 1|) - 5) + 1) 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(3|(2cos(1\u03c0x - 2) - 2) + 1| - 1)^2 - 1(3|(2cos(1\u03c0x - 2) - 2) + 1| - 1) + 2 and g(x) = 1e^(2(4x^2 - 1x - 4)) + 3 between the vertical lines x = 0.3 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(-2cos(3\u03c0(-5x - 1)) + 1)| + 2) + 1)/(2(-1|(-2cos(3\u03c0(-5x - 1)) + 1)| + 2) - 3), g(x) = 3(-3(1|x - 3| - 1)^2 - 4(1|x - 3| - 1) - 5) - 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": "8.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(3(-3(-1e^(2x))^2 + 2(-1e^(2x)) + 1) + 2))/(-2(3(-3(-1e^(2x))^2 + 2(-1e^(2x)) + 1) + 2) + 3) and g(x) = 5(1sin(3\u03c0(-1|x + 2| + 3) + 2))^2 - 4(1sin(3\u03c0(-1|x + 2| + 3) + 2)) - 5 from x = -3.3 to x = -2.8. 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) = 3|((1(-3x - 4) + 1)/(1(-3x - 4) - 2)) - 2| - 2 and g(x) = 3cos(3\u03c0(-1x^2 - 3x) + 2) - 2 between the vertical lines x = -5.0 and x = -4.9. 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) = (-3(5(1|(-3x^2 + 2x + 5) - 3| + 3) - 5) + 2)/(-2(5(1|(-3x^2 + 2x + 5) - 3| + 3) - 5) - 2) and g(x) = 1(3|(-3x - 5) + 3| - 1)^2 - 5(3|(-3x - 5) + 3| - 1) + 4 between the vertical lines x = -0.5 and x = -0.1. 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) = 2(1cos(1\u03c0(-1x^2 - 1) + 1) - 1) + 2, g(x) = 3(-3sin(3\u03c0x + 2) - 3) - 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2|(2cos(3\u03c0((-2x - 1)/(1x + 1)) + 2) - 2)| + 3)^2 - 3(-2|(2cos(3\u03c0((-2x - 1)/(1x + 1)) + 2) - 2)| + 3) - 3 and g(x) = 1|((-2(1e^(-1x)) + 1)/(-2(1e^(-1x)) + 1)) - 3| + 1 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1|((1(1x^2 + 4x + 1) + 2)/(2(1x^2 + 4x + 1) - 1)) - 3|) + 1 and g(x) = 2(5(-1|x + 2| + 2)^2 + 1(-1|x + 2| + 2)) - 4 from x = -3.9 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(3|((3(4x - 1) + 1)/(1(4x - 1))) - 3| - 3)^2 - 5(3|((3(4x - 1) + 1)/(1(4x - 1))) - 3| - 3) - 1 and g(x) = (3(5(-4x^2 - 5x + 1) - 5) - 2)/(1(5(-4x^2 - 5x + 1) - 5) + 2) between the vertical lines x = -1.2 and x = -0.3. 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": "Calculate the area enclosed between the functions f(x) = 2|(-1((1(2x^2 - 5x - 1) + 3)/(-2(2x^2 - 5x - 1) - 3)) + 1) - 3| - 2 and g(x) = -1|(-2cos(1\u03c0(-3x - 1) + 3) - 3) + 3| + 3 from x = 0.7 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) = (3(-1(4x - 2)^2 + 5(4x - 2) - 3))/(2(-1(4x - 2)^2 + 5(4x - 2) - 3) + 1) and g(x) = -5((1x - 2)/(-1x - 3)) - 2 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": "4.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(-1(1|((1x + 3)/(-2x - 3)) - 3| - 3)) + 2 and g(x) = 2e^(-1(-1x + 5)) - 1 between the vertical lines x = -2.0 and x = -1.6. 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": "Calculate the area enclosed between the functions f(x) = (-1(-3|(-3(3x^2 + 2) + 5)| + 1) + 3)/(-2(-3|(-3(3x^2 + 2) + 5)| + 1) - 3) and g(x) = -3(-1cos(2\u03c0((-2x - 3)/(3x + 2)) + 3) - 1)^2 + 1(-1cos(2\u03c0((-2x - 3)/(3x + 2)) + 3) - 1) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((-2(3sin(1\u03c0x - 3)) - 2)/(2(3sin(1\u03c0x - 3)) - 1)) - 5 and g(x) = -1(-5x + 3)^2 - 5(-5x + 3) - 5 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": "16.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2e^(1((2(3|x + 1| - 3))/(-2(3|x + 1| - 3) + 3))) + 3, g(x) = -2|(-5x^2 + 2x - 5) + 2| - 1, x = -2.4, 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": "76.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|((1(2x^2 + 1x - 5) - 1)/(1(2x^2 + 1x - 5)))|) + 5 and g(x) = (-1(2(-3x^2 - 1x - 4) + 3) - 3)/(1(2(-3x^2 - 1x - 4) + 3) + 1) between the vertical lines x = 1.3 and x = 1.4. 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": "Calculate the area enclosed between the functions f(x) = -1|(1sin(2\u03c0((3(-1x^2 - 3x + 3) - 3)/(-3(-1x^2 - 3x + 3) + 2)) + 2) - 3) + 1| + 2 and g(x) = -1|(-3(2sin(1\u03c0x - 2) + 2) + 1) - 3| + 3 from x = -3.6 to x = -3.5. 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) = (-1(-3|(-1(3x + 4)^2 - 2(3x + 4)) - 2| - 3) + 1)/(1(-3|(-1(3x + 4)^2 - 2(3x + 4)) - 2| - 3) - 3) and g(x) = (-2(2sin(3\u03c0(2x + 2) + 1) + 3) + 1)/(1(2sin(3\u03c0(2x + 2) + 1) + 3) + 3) between the vertical lines x = 3.3 and x = 3.4. 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) = 1|((1(4(-2sin(1\u03c0x - 3) + 3) + 3) + 1)/(2(4(-2sin(1\u03c0x - 3) + 3) + 3) - 3)) + 1| - 2, g(x) = -2cos(3\u03c0(-3|(-5x^2 - 2x - 4) - 2|) - 2) - 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-2(4(-3|x + 2| - 3)^2 - 1(-3|x + 2| - 3) + 5) - 2)/(-3(4(-3|x + 2| - 3)^2 - 1(-3|x + 2| - 3) + 5) + 2)) - 5, g(x) = -5(-5(1|x - 3| - 2) - 4)^2 + 1(-5(1|x - 3| - 2) - 4) + 3, x = 1.6, 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": "2.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1|(-1(3cos(1\u03c0x - 3))^2 + 4(3cos(1\u03c0x - 3)) - 1) + 2| + 3) - 1)/(-3(-1|(-1(3cos(1\u03c0x - 3))^2 + 4(3cos(1\u03c0x - 3)) - 1) + 2| + 3) + 4) and g(x) = (-3(1(-3|x + 2| + 2)^2 + 1(-3|x + 2| + 2) + 2))/(1(1(-3|x + 2| + 2)^2 + 1(-3|x + 2| + 2) + 2)) from x = -1.6 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) = 3sin(1\u03c0(5((3(3x^2 + 5x) + 2)/(2(3x^2 + 5x) - 1)) - 5) + 3) + 2, g(x) = -4(3(3|x + 2|)^2 - 4(3|x + 2|)) - 1, 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3(2cos(3\u03c0x - 2) + 3)^2 + 2(2cos(3\u03c0x - 2) + 3) + 3) + 1)/(2(-3(2cos(3\u03c0x - 2) + 3)^2 + 2(2cos(3\u03c0x - 2) + 3) + 3) - 1) and g(x) = 3e^(-1(-1x - 4)) - 2 between the vertical lines x = -4.9 and x = -4.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(2\u03c0(1|(3x^2 - 1x - 2) + 3| + 3) - 3), g(x) = 2sin(1\u03c0(1x - 3) - 2) - 2, x = 1.7, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(2cos(3\u03c0(3((1x - 2)/(1x + 3))^2 - 3((1x - 2)/(1x + 3)) + 4) + 2) - 3) - 3| - 2 and g(x) = -1(3e^(-1((3x + 3)/(1x))) - 1)^2 - 5(3e^(-1((3x + 3)/(1x))) - 1) between the vertical lines x = -3.1 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": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-4((-1(2x^2 - 3x - 3) - 2)/(2(2x^2 - 3x - 3) + 3)) - 4) - 2| + 3 and g(x) = 2|((2(1e^(2x) - 2) - 3)/(3(1e^(2x) - 2) - 2)) + 2| - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((2(3|(-1x^2 + 5x - 3) + 2| - 1) + 1)/(-1(3|(-1x^2 + 5x - 3) + 2| - 1))) - 3 and g(x) = -5(1|(1x^2 - 3x - 5)| + 1) + 3 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": "10.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(3sin(1\u03c0((-1x + 2)/(3x)) + 1) - 1) + 2, g(x) = -2cos(2\u03c0(-3x^2 - 3x - 3) + 1) - 3, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3((-2(2|x + 1| - 2))/(1(2|x + 1| - 2) - 2))^2 + 5) and g(x) = 2e^(1(-4(3x^2 + 3x - 5) + 2)) from x = -2.4 to x = -1.9. 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) = 1cos(1\u03c0(-1(-1|x - 2| + 1)^2 - 2(-1|x - 2| + 1) - 1) - 1) - 2 and g(x) = -3(1x + 2)^2 + 3(1x + 2) between the vertical lines x = -2.6 and x = -2.5. 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(1|(5x^2 + 3x) - 2| - 3) + 1)/(2(1|(5x^2 + 3x) - 2| - 3) - 1), g(x) = 5(-2x^2 - 4x + 4) + 3, x = -2.8, 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": "25.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(-1cos(1\u03c0(-4x^2 - 1x) + 3) + 2) + 2)/(3(-1cos(1\u03c0(-4x^2 - 1x) + 3) + 2) - 2) and g(x) = -1cos(2\u03c0((2x + 3)/(-2x + 1)) + 3) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-4(-3x + 4)^2 - 5(-3x + 4) - 4) + 2)/(3(-4(-3x + 4)^2 - 5(-3x + 4) - 4)) and g(x) = -2(-1cos(3\u03c0x + 3))^2 + 2(-1cos(3\u03c0x + 3)) + 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2(1|((1x)/(2x + 3)) + 3| - 3)^2 - 1) + 3, g(x) = (-1(-2e^(1(-4x^2 + 4x - 4)) - 3) + 1)/(-1(-2e^(1(-4x^2 + 4x - 4)) - 3) - 2), x = -1.4, 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": "12.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(1((-3x + 1)/(-2x + 3))^2 - 3((-3x + 1)/(-2x + 3)) + 3) + 1) + 2 and g(x) = 3e^(-1(-4x^2 + 1x)) - 1 between the vertical lines x = -0.0 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) = 2|(-1(1e^(-1(4x^2 - 5x - 2)) - 2) - 3)| - 3 and g(x) = 1(-2((3x)/(1x - 3)) + 4)^2 + 1(-2((3x)/(1x - 3)) + 4) - 4 between the vertical lines x = -2.4 and x = 0.0. 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) = 4(3cos(1\u03c0((-2x + 2)/(1x - 2))) + 2)^2 + 5(3cos(1\u03c0((-2x + 2)/(1x - 2))) + 2) + 5, g(x) = 1(1x + 5)^2 + 5(1x + 5) + 1, 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": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(1(5x^2 + 5x - 3) - 2) + 3)/(1(1(5x^2 + 5x - 3) - 2) - 3), g(x) = 2(2sin(1\u03c0x + 2) - 2), x = -1.7, 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": "11.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2|(5(3x - 1)^2 - 3(3x - 1)) + 2| + 3) + 2)/(-2(2|(5(3x - 1)^2 - 3(3x - 1)) + 2| + 3) - 3) and g(x) = (-3(1e^(-1(3x^2 - 1x - 2)) + 1) + 2)/(-2(1e^(-1(3x^2 - 1x - 2)) + 1) - 2) from x = 0.2 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": "Calculate the area enclosed between the functions f(x) = (2(2(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) - 2) - 2)/(2(2(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) - 2) + 3) and g(x) = 1|(-1x^2 + 4x - 1) - 1| + 3 from x = -0.6 to x = 0.6. 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) = (-2(-1e^(-1(5(1|x - 1| + 3) + 4)) + 2))/(-3(-1e^(-1(5(1|x - 1| + 3) + 4)) + 2) - 1) and g(x) = 2|(-2cos(2\u03c0(3x) + 3)) + 1| - 1 from x = 4.4 to x = 4.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = 4((-3(1x^2 + 5x + 4))/(3(1x^2 + 5x + 4) + 2)) - 4 and g(x) = -2|((1x - 1)/(1x)) + 1| + 2 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": "86.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-1e^(-1(-2|(1x^2 - 4x - 4)|)) + 1) - 1 and g(x) = -1(1sin(1\u03c0(3|x + 1| - 1) - 1) + 2)^2 + 2(1sin(1\u03c0(3|x + 1| - 1) - 1) + 2) + 2 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": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(1(-4x - 2)) + 1) - 1)/(2(-1e^(1(-4x - 2)) + 1) - 1), g(x) = -4((-2x - 3)/(2x + 2)) + 2, 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": "96.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2cos(2\u03c0(-3|(2x^2 - 3x + 3) + 1| + 3) + 1) - 3 and g(x) = -5(1sin(2\u03c0x - 1) + 1) + 3 from x = 3.2 to x = 3.3000000000000003. 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) = -4(1cos(2\u03c0(3|x + 2| + 3) + 1) + 3)^2 + 1, g(x) = -2|(-1e^(-2x) + 3) - 2| - 2, x = -1.5, 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2(-1x - 1)^2 - 3(-1x - 1) + 1) - 3| + 3 and g(x) = 1(2|x + 1| - 2) + 3 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3((-3x - 3)/(2x - 3)) + 3)^2 - 1(3((-3x - 3)/(2x - 3)) + 3) - 3 and g(x) = -2|((-3x + 1)/(-1x))| + 2 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": "48.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1((-2(-1(1|x + 1| - 3)^2 - 2(1|x + 1| - 3) - 1) - 1)/(2(-1(1|x + 1| - 3)^2 - 2(1|x + 1| - 3) - 1))) and g(x) = (-3(-3cos(1\u03c0(1x^2 + 5x) + 2) - 2) + 2)/(-2(-3cos(1\u03c0(1x^2 + 5x) + 2) - 2) - 3) 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": "Determine the area of the region enclosed by the graphs of f(x) = (3(-5(-2cos(1\u03c0(3x - 4) - 3) - 2)^2 + 3(-2cos(1\u03c0(3x - 4) - 3) - 2) + 2) + 2)/(1(-5(-2cos(1\u03c0(3x - 4) - 3) - 2)^2 + 3(-2cos(1\u03c0(3x - 4) - 3) - 2) + 2) - 3) and g(x) = 3|(-4(1x + 3)^2 + 2(1x + 3) - 2)| - 3 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(3|(3x^2 - 3x - 2) - 1| - 3) + 2, g(x) = 1(-2e^(-1x) + 2) + 5, 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((1(-1|x - 1| + 2) - 1)/(1(-1|x - 1| + 2) - 3)) + 5, g(x) = 2e^(-1(1|x + 1| - 2)) - 1, x = -2.4, 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": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(-1((-2x - 3)/(3x - 2)) + 4)^2 + 4(-1((-2x - 3)/(3x - 2)) + 4) + 5 and g(x) = -2sin(2\u03c0(3x^2 + 1x + 1)) + 3 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((2(3|x - 3| + 3))/(-2(3|x - 3| + 3) - 2))^2 - 2((2(3|x - 3| + 3))/(-2(3|x - 3| + 3) - 2)) - 4, g(x) = -1(3x^2 + 4x - 3) - 3, x = -1.9, 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": "7.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((-3(3x - 2) - 1)/(1(3x - 2)))^2 + 3((-3(3x - 2) - 1)/(1(3x - 2))) - 4 and g(x) = -1cos(3\u03c0((-1x)/(-2x - 2))) + 3 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3cos(3\u03c0(1|x - 2| - 2) - 1) - 3) + 3)/(2(3cos(3\u03c0(1|x - 2| - 2) - 1) - 3)), g(x) = 1(2|x - 1| + 1) - 3, x = 0.7, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1cos(1\u03c0(-5(-3x^2 + 5x - 4) - 1) - 2) + 3) + 2| + 3 and g(x) = -5(2|(-2sin(2\u03c0x + 2) + 1)| - 3) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(3|((-3x + 1)/(2x - 1))| - 3) + 3, g(x) = 3|(-1x - 1) + 2| - 1, x = -1.9, 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": "3.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3|(-3x + 1) + 3|) - 3)/(2(3|(-3x + 1) + 3|) + 2), g(x) = 3(-1|x + 3| + 1)^2 - 3(-1|x + 3| + 1) - 5, x = -4.9, 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": "17.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(-2|(5x^2 + 5x - 5) + 3| + 2) - 5, g(x) = 1e^(2((1x)/(1x - 2))) - 2, 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) = -4(2cos(2\u03c0(2(1|x - 2|) - 2) + 2))^2 - 1, g(x) = -5((-2(-4x^2 - 3x - 5) + 3)/(-1(-4x^2 - 3x - 5) - 2)) + 1, 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(3\u03c0(2(-2|(4x - 4) - 3|)^2 - 2(-2|(4x - 4) - 3|) + 1) - 1) - 2, g(x) = -3cos(1\u03c0(5(-2|x + 2|)^2 + 5(-2|x + 2|))) + 3, x = 4.3, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-3(1(-5x^2 + 4x + 1) - 4) - 1)/(-2(1(-5x^2 + 4x + 1) - 4) + 3)) - 2| - 2 and g(x) = 5(3(-3e^(-1x) + 2)^2 + 3(-3e^(-1x) + 2)) - 5 between the vertical lines x = -0.1 and 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) = -1|(-5(-1((1x + 2)/(2x + 2))^2 + 3((1x + 2)/(2x + 2)) - 1) - 5) - 1| + 2 and g(x) = 5(-1(-2|x| + 3)^2 + 1) + 4 from x = -0.8 to x = -0.7000000000000001. 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) = 3cos(1\u03c0(2(-1((-2x - 2)/(-1x + 2)) + 1)^2 - 3(-1((-2x - 2)/(-1x + 2)) + 1)) - 3) + 1 and g(x) = 1|(-1(-3sin(2\u03c0x - 2))^2 + 2(-3sin(2\u03c0x - 2)) + 2) + 1| - 2 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(3\u03c0(-1|((-1(-2x^2 - 1x + 5))/(-1(-2x^2 - 1x + 5) - 1))| + 3) - 1) - 3 and g(x) = 3cos(1\u03c0(1|((3x + 2)/(1x + 1))| - 2) + 3) - 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3sin(3\u03c0((-1x - 3)/(2x + 2)) - 1) + 3)^2 - 4(-3sin(3\u03c0((-1x - 3)/(2x + 2)) - 1) + 3) + 5 and g(x) = (1(-1|x + 2| + 1) + 3)/(2(-1|x + 2| + 1) - 1) from x = -2.1 to x = -1.8. 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": "Calculate the area enclosed between the functions f(x) = (3(-1(-2|(3x^2 - 3) + 3| + 1) + 1) + 2)/(2(-1(-2|(3x^2 - 3) + 3| + 1) + 1) - 1) and g(x) = 2cos(2\u03c0(-3(-1x^2 + 3x) + 2) - 3) + 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-3|((-2x - 3)/(-1x + 2))| + 2)^2 - 3(-3|((-2x - 3)/(-1x + 2))| + 2) + 4 and g(x) = (1(-2x - 1))/(1(-2x - 1) + 3) 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1|(-3x + 4) + 2| + 1) + 2)/(1(-1|(-3x + 4) + 2| + 1)) and g(x) = -1sin(2\u03c0((2x + 2)/(1x + 3))) + 2 from x = 1.9 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": "Calculate the area enclosed between the functions f(x) = 1|(2(-3x^2 + 1x - 1) - 1) + 2| - 3 and g(x) = 2(1cos(3\u03c0x + 1) + 3) - 5 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(5(-4(-1|x| - 2)^2 - 4(-1|x| - 2)) + 4))/(1(5(-4(-1|x| - 2)^2 - 4(-1|x| - 2)) + 4)), g(x) = -2((-2(2x + 4) + 2)/(-1(2x + 4) + 3))^2 + 5((-2(2x + 4) + 2)/(-1(2x + 4) + 3)) + 1, x = -1.5, 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": "-11.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2|(1cos(2\u03c0x + 3) - 3)| + 1))/(-2(2|(1cos(2\u03c0x + 3) - 3)| + 1) - 2) and g(x) = (2(3|x - 3| - 1) - 1)/(3(3|x - 3| - 1) - 1) between the vertical lines x = 2.7 and x = 3.3. 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) = (1(-3(1e^(2x) - 2)^2 - 4(1e^(2x) - 2) + 3) - 2)/(2(-3(1e^(2x) - 2)^2 - 4(1e^(2x) - 2) + 3)), g(x) = (-2(-1x^2 + 4x - 1) + 3)/(1(-1x^2 + 4x - 1)), x = 0.6, 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": "3.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2sin(1\u03c0((-1x)/(1x - 3)) + 1) + 2)^2 + 5(-2sin(1\u03c0((-1x)/(1x - 3)) + 1) + 2) - 4 and g(x) = (-1(-1cos(1\u03c0x - 1) - 3) - 3)/(2(-1cos(1\u03c0x - 1) - 3) + 1) between the vertical lines x = 4.0 and x = 4.2. 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) = 1e^(2(5(-2|x| + 2)^2 + 3(-2|x| + 2))) - 2, g(x) = 3e^(-2(-5x + 5)) + 2, x = 0.9, 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": "83.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-3(-5x - 3)^2 - 4(-5x - 3) + 3) - 2|, g(x) = -1|((-2x - 2)/(3x)) + 3| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(2\u03c0(-1|((2x - 1)/(1x + 3)) + 1| + 2) - 1) + 2 and g(x) = 3(1sin(3\u03c0x + 1) - 1)^2 + 5(1sin(3\u03c0x + 1) - 1) + 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": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2|(-4(1x^2 + 5x + 5) - 2)|) - 2)/(1(2|(-4(1x^2 + 5x + 5) - 2)|)) and g(x) = -3|(-2(-1cos(3\u03c0x))^2 + 3(-1cos(3\u03c0x)) - 2) - 2| - 3 between the vertical lines x = -3.4 and x = -3.3. 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) = 2|(2cos(1\u03c0(-4x^2 - 5x + 2) - 2) - 3) - 2| - 1 and g(x) = 2((-1x + 2)/(1x))^2 - 4((-1x + 2)/(1x)) - 2 from x = -3.3 to 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": "Calculate the area enclosed between the functions f(x) = (3(4(-2cos(1\u03c0x - 3) - 1) - 2) - 1)/(-2(4(-2cos(1\u03c0x - 3) - 1) - 2) - 3) and g(x) = 2(-2cos(3\u03c0x + 2) - 1) - 2 from x = 4.1 to x = 4.2. 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) = (-1(5(-2|x - 1|)^2 - 2) + 3)/(1(5(-2|x - 1|)^2 - 2) - 2) and g(x) = -4(3x - 2)^2 + 3 from x = 0.5 to x = 1.0. 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": "Find the area of the region bounded by the curves f(x) = -3(-2sin(2\u03c0(1x^2 - 2x + 1) - 2) + 3) - 1, g(x) = -1(-1x - 2)^2 - 4(-1x - 2) + 5, x = -4.6, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3cos(3\u03c0(3|x + 2| + 2) + 2))^2 - 3 and g(x) = -1(-2|x - 3| - 1) + 2 between the vertical lines x = 2.5 and x = 2.6. 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": "Calculate the area enclosed between the functions f(x) = (-3(-3(1sin(1\u03c0x - 2) + 2)^2 - 1(1sin(1\u03c0x - 2) + 2) + 3) - 1)/(-3(-3(1sin(1\u03c0x - 2) + 2)^2 - 1(1sin(1\u03c0x - 2) + 2) + 3) - 1) and g(x) = -3sin(2\u03c0((-2x)/(2x + 1)) + 2) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(3|(-2(-1sin(3\u03c0x + 3) + 2) + 5)| + 1) + 3)/(-2(3|(-2(-1sin(3\u03c0x + 3) + 2) + 5)| + 1) + 3), g(x) = -2(-5((-2x)/(2x - 1)))^2 - 2(-5((-2x)/(2x - 1))) + 4, x = -3.2, 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": "8.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1|((2x + 1)/(-2x + 3))| + 2)^2 - 4(1|((2x + 1)/(-2x + 3))| + 2) - 5, g(x) = -2((-2x - 1)/(2x + 2))^2 - 1((-2x - 1)/(2x + 2)) - 1, 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": "-12.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3sin(1\u03c0(1(-3|x + 1| + 1) + 5) - 1) + 2 and g(x) = -2|((2x - 3)/(1x - 2)) + 1| + 3 between the vertical lines x = 1.6 and x = 1.8. 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": "Determine the area of the region enclosed by the graphs of f(x) = -1((1(1|x - 3| - 1) + 3)/(-1(1|x - 3| - 1) - 2))^2 + 3((1(1|x - 3| - 1) + 3)/(-1(1|x - 3| - 1) - 2)) and g(x) = 4(2e^(-1x) - 2) - 2 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(5(2|x - 3|) + 1) - 1)/(-1(5(2|x - 3|) + 1) - 3), g(x) = -1((3x + 2)/(-2x + 3))^2 + 5((3x + 2)/(-2x + 3)) - 5, x = 0.2, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1((2(3|x - 1| + 2) - 1)/(1(3|x - 1| + 2) + 3)) - 3)^2 + 1, g(x) = -1|((-3(-3sin(1\u03c0x + 1)) - 2)/(-1(-3sin(1\u03c0x + 1)) - 2)) - 1|, 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": "25.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3((1(2|x - 1| + 3) + 3)/(-3(2|x - 1| + 3) - 2)) + 4, g(x) = 1(-2|x - 1| - 1)^2 + 5(-2|x - 1| - 1) + 3, x = -1.0, 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": "17.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((2(-2sin(2\u03c0(1x^2 + 1) + 2)) - 1)/(-2(-2sin(2\u03c0(1x^2 + 1) + 2)) + 3)) - 2| + 2 and g(x) = 5(-3e^(1(2x + 3)) - 3)^2 - 2(-3e^(1(2x + 3)) - 3) + 3 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": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1(-4(-1x^2 + 2x + 3) + 4) - 3)/(-1(-4(-1x^2 + 2x + 3) + 4))) + 1| - 2 and g(x) = -5(3|(1x^2 + 5x + 4) - 3| + 1) + 1 between the vertical lines x = -0.7 and x = -0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((1(1cos(1\u03c0(3x^2 - 2x - 4) + 1) - 3) - 2)/(3(1cos(1\u03c0(3x^2 - 2x - 4) + 1) - 3) - 2)) - 2 and g(x) = 1((-1(1x^2 + 3x + 2) + 1)/(3(1x^2 + 3x + 2) - 2)) + 2 from x = -2.4 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(1(1|(-2x - 5) - 2| + 2)^2 + 3(1|(-2x - 5) - 2| + 2) + 2) - 3) - 2, g(x) = 1((-2(-1cos(1\u03c0x - 1)) - 1)/(-1(-1cos(1\u03c0x - 1)) + 3))^2 + 3((-2(-1cos(1\u03c0x - 1)) - 1)/(-1(-1cos(1\u03c0x - 1)) + 3)) - 3, x = 4.4, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-1(-2|x - 1| - 1) + 4) - 3)/(1(-1(-2|x - 1| - 1) + 4) + 3) and g(x) = -1(3sin(1\u03c0x - 3) - 1)^2 + 2(3sin(1\u03c0x - 3) - 1) + 4 between the vertical lines x = 0.0 and x = 0.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3sin(2\u03c0((2x - 1)/(-3x)) - 3) + 3) and g(x) = -3cos(1\u03c0(1x^2 - 5x + 1) + 1) - 2 between the vertical lines x = 1.3 and x = 1.8. 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) = 1|(1((-3(3x + 1) - 3)/(1(3x + 1) + 1))^2 + 5((-3(3x + 1) - 3)/(1(3x + 1) + 1)) - 2) + 2| and g(x) = 1((2(1|x - 3| - 2) - 1)/(-3(1|x - 3| - 2) + 2))^2 + 3((2(1|x - 3| - 2) - 1)/(-3(1|x - 3| - 2) + 2)) - 4 between the vertical lines x = 0.3 and x = 0.4. 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) = -3|(3((2(-3cos(1\u03c0x - 1) - 3))/(2(-3cos(1\u03c0x - 1) - 3)))^2 - 3((2(-3cos(1\u03c0x - 1) - 3))/(2(-3cos(1\u03c0x - 1) - 3))) - 5) + 2| - 3 and g(x) = -3((2(-1x^2 - 2x + 1) + 1)/(2(-1x^2 - 2x + 1) + 2)) + 4 from x = -2.8 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(-2(1(2x^2 - 1))) + 1, g(x) = -1(2x^2 + 5x - 5) - 1, x = -3.0, 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": "33.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(2sin(3\u03c0((3(-3|x| - 2) + 1)/(1(-3|x| - 2) - 3))) + 3)^2 + 2(2sin(3\u03c0((3(-3|x| - 2) + 1)/(1(-3|x| - 2) - 3))) + 3) + 3 and g(x) = -1e^(2(1(-1x^2 + 2x + 2) - 4)) - 2 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": "33.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(1cos(2\u03c0(2|x|)) - 1) - 2, g(x) = 1|(1e^(-1x))| + 1, x = 3.7, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1((1x)/(-2x - 1)) - 5)^2 + 2 and g(x) = -2|((3x + 2)/(-3x + 1)) - 3| - 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": "87.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-1(-1x)^2 + 4(-1x) + 4))/(-1(-1(-1x)^2 + 4(-1x) + 4) + 2) and g(x) = -2(-1sin(3\u03c0x + 1) - 3) from x = -4.2 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1(-2x + 5) - 1)/(-1(-2x + 5) + 2)) + 1| + 3 and g(x) = -1e^(1(4x^2 - 4x + 2)) + 1 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": "66.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-2e^(2(5(-3|x - 3| + 3) + 1)) - 3)^2 and g(x) = -2(-2|(-3cos(3\u03c0x - 3) - 3) + 2| - 3) - 4 from x = -3.7 to x = -3.0. 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": "Calculate the area enclosed between the functions f(x) = 1(1((1x + 1)/(-3x)))^2 - 5(1((1x + 1)/(-3x))) + 2 and g(x) = 3|(-3cos(2\u03c0x + 3) - 1) - 3| - 3 from x = -3.8 to x = -3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-2|(-1x^2 + 2x + 3) + 2| - 3) - 1)/(-1(-2|(-1x^2 + 2x + 3) + 2| - 3) - 2) and g(x) = -2e^(-1(1x^2 + 5x + 3)) + 3 between the vertical lines x = -4.0 and x = -1.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((3(-1(-1|x - 3| + 2)^2 - 1(-1|x - 3| + 2)) - 2)/(3(-1(-1|x - 3| + 2)^2 - 1(-1|x - 3| + 2)) + 3)) + 1 and g(x) = 1(-3|(1x^2 + 2x - 5)| - 1) - 5 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": "33.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-3(1sin(2\u03c0(-5x + 1) + 3))^2 + 4(1sin(2\u03c0(-5x + 1) + 3)) + 5) + 3)/(2(-3(1sin(2\u03c0(-5x + 1) + 3))^2 + 4(1sin(2\u03c0(-5x + 1) + 3)) + 5)) and g(x) = 3(3((3x - 3)/(1x))^2 - 1((3x - 3)/(1x)) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-1sin(3\u03c0((1x + 3)/(1x + 2))) - 1) - 2| - 3 and g(x) = -5((1x - 3)/(-1x + 3))^2 + 4((1x - 3)/(-1x + 3)) from x = -1.7 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((-1(-1sin(2\u03c0x - 3)) - 2)/(-1(-1sin(2\u03c0x - 3)) + 2))^2 - 5((-1(-1sin(2\u03c0x - 3)) - 2)/(-1(-1sin(2\u03c0x - 3)) + 2)) - 3 and g(x) = 1sin(3\u03c0(1x - 5) + 3) + 3 between the vertical lines x = 2.9 and x = 3.5. 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": "Find the area of the region bounded by the curves f(x) = (-2(-2sin(1\u03c0(-1|x + 1| + 2))) + 2)/(-2(-2sin(1\u03c0(-1|x + 1| + 2))) - 1), g(x) = -3|(-1x + 3) - 1|, x = 4.0, 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": "12.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(2((1(2sin(2\u03c0x - 3) - 2) + 3)/(3(2sin(2\u03c0x - 3) - 2) + 1))^2 + 4((1(2sin(2\u03c0x - 3) - 2) + 3)/(3(2sin(2\u03c0x - 3) - 2) + 1)) - 3) + 1 and g(x) = -3cos(2\u03c0(3(3|x + 1| - 2) + 2) - 1) + 3 from x = -1.7 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": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-1|x - 3| + 1) - 3)/(2(-1|x - 3| + 1) + 1))^2 - 4((-2(-1|x - 3| + 1) - 3)/(2(-1|x - 3| + 1) + 1)) - 4 and g(x) = 1|(-4x - 2)| - 2 between the vertical lines x = -0.3 and x = 1.1. 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) = (-2(3cos(1\u03c0(-4x + 2) + 3) - 2) - 3)/(3(3cos(1\u03c0(-4x + 2) + 3) - 2) - 1) and g(x) = (3(-1cos(2\u03c0x - 1) - 2))/(2(-1cos(2\u03c0x - 1) - 2) + 3) from x = -3.8 to x = -3.7. 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) = -1|(-1(4x^2 + 1x + 3)) - 3| + 3, g(x) = -3sin(3\u03c0(-5x + 3)) - 2, x = -0.5, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(4(1|(-2x + 1) + 3| + 1)^2 + 1(1|(-2x + 1) + 3| + 1)) + 2)/(-2(4(1|(-2x + 1) + 3| + 1)^2 + 1(1|(-2x + 1) + 3| + 1)) + 1), g(x) = 1|(2cos(3\u03c0((1x - 2)/(1x - 3)))) + 1| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(3(2(-2|x + 1| + 3)^2 + 3(-2|x + 1| + 3) - 3) - 5) + 3)/(1(3(2(-2|x + 1| + 3)^2 + 3(-2|x + 1| + 3) - 3) - 5) - 3), g(x) = (3(-1(1x + 1)^2 - 1(1x + 1) - 2) + 2)/(1(-1(1x + 1)^2 - 1(1x + 1) - 2) + 1), x = -1.9, 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(1\u03c0(-1(1x^2 - 5x - 1) - 2) + 3) - 3 and g(x) = 2|(2x^2 - 1x - 3) + 1| - 3 from x = -1.0 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": "Find the area of the region bounded by the curves f(x) = (2(2cos(2\u03c0(1x^2 + 4x + 5) + 2) + 1))/(2(2cos(2\u03c0(1x^2 + 4x + 5) + 2) + 1) + 3), g(x) = (3(1e^(1x) + 2) - 3)/(-1(1e^(1x) + 2) - 3), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2(3|x + 3| + 1)^2 + 2(3|x + 3| + 1) + 4) + 2)/(3(-2(3|x + 3| + 1)^2 + 2(3|x + 3| + 1) + 4) - 2), g(x) = (-3(1sin(2\u03c0x - 2) - 1) - 2)/(-2(1sin(2\u03c0x - 2) - 1) - 3), 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1|(-2e^(-1(-1x^2 - 2x - 2)) - 1) - 2| - 3) - 3 and g(x) = (2(-3sin(2\u03c0(1x + 4) - 3) + 3))/(3(-3sin(2\u03c0(1x + 4) - 3) + 3) - 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1((-2(-4(3|x + 2| + 3)^2 - 1(3|x + 2| + 3) + 2) + 3)/(2(-4(3|x + 2| + 3)^2 - 1(3|x + 2| + 3) + 2) - 3)) + 1 and g(x) = 3|(-2e^(-2((-1x - 1)/(-1x - 2))) + 1) + 2| - 3 from x = -1.3 to 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": "Calculate the area enclosed between the functions f(x) = 3e^(1(-2(2x - 5)^2 - 2)) - 2 and g(x) = 2cos(1\u03c0(1x + 2) + 3) - 1 from x = 2.4 to x = 3.7. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2(1sin(1\u03c0(-2|(-3x^2 + 3) - 1| - 3) + 3) + 2) + 5 and g(x) = -1((2(3|x - 1| - 2))/(-1(3|x - 1| - 2) + 3)) + 4 between the vertical lines x = 4.6 and x = 4.699999999999999. 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(-5((3(2|x - 3|) + 3)/(-1(2|x - 3|) + 2)) - 2) + 1) - 1 and g(x) = 2(1cos(1\u03c0(-3x - 5) - 3) - 2)^2 + 1(1cos(1\u03c0(-3x - 5) - 3) - 2) - 5 between the vertical lines x = 3.9 and x = 4.1. 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) = (-1(-3sin(1\u03c0(-5x^2 - 5x - 3) + 1)) - 2)/(3(-3sin(1\u03c0(-5x^2 - 5x - 3) + 1)) + 3), g(x) = (-2(-3|x - 2|))/(-2(-3|x - 2|) - 1), x = 4.1, and x = 4.199999999999999. 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|(1((-1(-2e^(-1x) - 1) + 1)/(2(-2e^(-1x) - 1) + 2)) + 2) - 1| - 3, g(x) = (-2(-3(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 5) - 1)/(-3(-3(-3|x + 1| + 2)^2 - 1(-3|x + 1| + 2) + 5) - 2), x = -1.3, 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(4(-5x^2 - 5x + 3) + 2) - 1)/(-2(4(-5x^2 - 5x + 3) + 2) - 1) and g(x) = -3|(1sin(1\u03c0x + 1) - 2) + 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(1(-3|x - 3| - 3) + 1) + 1)/(1(1(-3|x - 3| - 3) + 1) + 3), g(x) = -3sin(3\u03c0(1x^2 - 4x - 2) - 3) - 2, x = -2.7, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-2|((3(3cos(3\u03c0x - 3)) + 1)/(1(3cos(3\u03c0x - 3)) - 2)) - 2| + 3), g(x) = -1|(3sin(3\u03c0(-4x) - 2) - 1) + 1| - 1, x = 3.2, 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": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0((2(1x + 3) - 2)/(-1(1x + 3) + 3))) - 3 and g(x) = -2sin(3\u03c0(-3x + 5) - 3) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(-3(1(2e^(-2x) + 1) - 3)^2 + 3(1(2e^(-2x) + 1) - 3) - 1) + 2| + 3 and g(x) = (3(3cos(1\u03c0(-1x^2 + 2x - 1) - 3) - 1) + 3)/(1(3cos(1\u03c0(-1x^2 + 2x - 1) - 3) - 1) + 2) between the vertical lines x = 3.5 and x = 3.8. 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": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2((3(1e^(-1x) + 2) + 2)/(2(1e^(-1x) + 2) - 3))^2 + 4((3(1e^(-1x) + 2) + 2)/(2(1e^(-1x) + 2) - 3)) - 5) + 5 and g(x) = 2|(-2((-2x + 1)/(-2x)) - 1)| - 2 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": "42.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(5((1(-5x^2 - 1x - 4))/(-1(-5x^2 - 1x - 4) - 1)) + 1) - 1| and g(x) = (-2(-5(3cos(2\u03c0x + 1)) + 5) - 1)/(1(-5(3cos(2\u03c0x + 1)) + 5) + 3) from x = -2.0 to x = -1.3. 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": "Calculate the area enclosed between the functions f(x) = -1(3(-2|((2x - 3)/(-3x - 1)) - 1|)^2 + 2(-2|((2x - 3)/(-3x - 1)) - 1|) - 4) + 1 and g(x) = (-3(-1(-2|x + 1|)^2 - 2(-2|x + 1|) + 2) - 3)/(-2(-1(-2|x + 1|)^2 - 2(-2|x + 1|) + 2) - 1) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(1(2|(-2x - 4) + 3| + 2)) + 1 and g(x) = 5(-2e^(1x))^2 - 5(-2e^(1x)) - 4 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3(1sin(3\u03c0((-2(-1|x - 3| - 2))/(-2(-1|x - 3| - 2) - 3)) + 2) + 2) - 1, g(x) = -5(3cos(3\u03c0(-1x) + 1) + 2)^2 + 4(3cos(3\u03c0(-1x) + 1) + 2) - 2, 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": "18.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-3|(-2(-1x^2 - 1x - 1) + 4) + 1| + 1) - 3)/(2(-3|(-2(-1x^2 - 1x - 1) + 4) + 1| + 1) + 1) and g(x) = -3e^(-1(-1(2|x| - 1) + 1)) between the vertical lines x = -0.4 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": "Calculate the area enclosed between the functions f(x) = -3|(5((-3x - 3)/(-1x + 2))^2 - 3((-3x - 3)/(-1x + 2)) + 5) - 3| + 3 and g(x) = -2(-3e^(2x) - 3)^2 + 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": "-33227.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-4(-2cos(3\u03c0x - 2) + 2)^2 + 5(-2cos(3\u03c0x - 2) + 2) + 2) - 1, g(x) = (-1(1e^(2x)) + 3)/(-1(1e^(2x))), x = 0.1, 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": "Find the area of the region bounded by the curves f(x) = -1sin(3\u03c0(3((-2x + 3)/(3x - 1))^2 - 3) - 3) + 1, g(x) = 1(3cos(3\u03c0x + 3) + 3)^2 - 3(3cos(3\u03c0x + 3) + 3) - 1, x = -2.8, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(1\u03c0(-3(-3|((-2x - 1)/(-1x + 2)) - 2| - 3) - 4) + 3) + 2 and g(x) = 2sin(3\u03c0(-1|(3x - 2) + 2| - 1) + 2) + 1 between the vertical lines x = 1.5 and 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) = 3cos(2\u03c0(-3((-2x - 3)/(-3x))^2 - 1((-2x - 3)/(-3x)) + 1) - 3) + 3, g(x) = (-3(3|x - 3| - 2) + 1)/(-1(3|x - 3| - 2) + 2), x = -0.4, and x = -0.30000000000000004. 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((2(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2) + 1) + 3)/(2(-4(-2|x - 2| + 2)^2 + 3(-2|x - 2| + 2) + 1) - 1)) + 1 and g(x) = -4(2((-2x - 1)/(3x + 1))^2 + 3((-2x - 1)/(3x + 1)) - 2) + 3 from x = 0.9 to x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(1\u03c0(-3(2|x + 3| - 2) - 5) + 3) - 1 and g(x) = 4((2x)/(-2x + 1)) + 5 between the vertical lines x = 1.6 and x = 1.7. 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) = -1(1((-3x + 2)/(2x - 3))^2 - 1((-3x + 2)/(2x - 3))) + 1 and g(x) = -4(-2cos(2\u03c0x - 2) + 3) - 1 between the vertical lines x = 2.5 and x = 3.2. 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) = (2(-4(2|x + 2| + 3)^2 + 2(2|x + 2| + 3) + 3) + 3)/(1(-4(2|x + 2| + 3)^2 + 2(2|x + 2| + 3) + 3) - 3) and g(x) = -3(-3e^(2x) + 1)^2 - 5(-3e^(2x) + 1) 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": "Calculate the area enclosed between the functions f(x) = (-2(2|(-1e^(2x) - 1) - 2| + 1) - 1)/(2(2|(-1e^(2x) - 1) - 2| + 1) + 2) and g(x) = 2(3cos(2\u03c0x) - 2)^2 - 3(3cos(2\u03c0x) - 2) - 2 from x = -3.2 to 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": "Find the area of the region bounded by the curves f(x) = -2|((2(2(3x - 4)^2 + 1(3x - 4) - 3) + 3)/(3(2(3x - 4)^2 + 1(3x - 4) - 3) - 2)) - 2| + 1, g(x) = (2(5(3sin(3\u03c0x) + 1)^2 - 1(3sin(3\u03c0x) + 1) - 5) + 3)/(1(5(3sin(3\u03c0x) + 1)^2 - 1(3sin(3\u03c0x) + 1) - 5) - 3), 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(1(5x + 3)^2 + 4(5x + 3) + 3) - 2| - 2 and g(x) = (-2(-3x^2 + 2x + 3))/(1(-3x^2 + 2x + 3)) 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": "2.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|((-1(-1(-2x^2 - 1x + 1) - 2) - 2)/(-1(-1(-2x^2 - 1x + 1) - 2) - 1)) + 2| - 1 and g(x) = (3(-5(3|x + 1| - 3)^2 + 4(3|x + 1| - 3)) + 1)/(-2(-5(3|x + 1| - 3)^2 + 4(3|x + 1| - 3)) - 2) between the vertical lines x = -1.9 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2((1x - 3)/(2x - 1))^2 - 4((1x - 3)/(2x - 1)) - 3) + 3, g(x) = (-2(3x + 3) + 3)/(3(3x + 3) + 3), x = -1.4, 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": "21.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((1(-2x - 2) - 3)/(1(-2x - 2) - 2))^2 + 1((1(-2x - 2) - 3)/(1(-2x - 2) - 2)) - 5, g(x) = 3|((-3x + 2)/(-2x - 2)) - 1|, 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": "-6.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(2\u03c0(1(2(-3|x - 1| + 1) + 5)^2 - 4(2(-3|x - 1| + 1) + 5) - 5) - 1) + 3 and g(x) = (-2(3(-2x + 2)^2 + 4(-2x + 2) + 4) - 2)/(-1(3(-2x + 2)^2 + 4(-2x + 2) + 4) - 3) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2(1((-2x - 3)/(3x)) - 4)^2 - 4(1((-2x - 3)/(3x)) - 4) - 3) + 1| - 3 and g(x) = 1(-1|(2sin(3\u03c0x - 2) - 3) - 3| + 2)^2 + 4(-1|(2sin(3\u03c0x - 2) - 3) - 3| + 2) 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((-1(2|(5x + 2) - 1| - 3) + 3)/(-1(2|(5x + 2) - 1| - 3) - 2))^2 - 1((-1(2|(5x + 2) - 1| - 3) + 3)/(-1(2|(5x + 2) - 1| - 3) - 2)) - 1 and g(x) = 2(1|(-2x^2 - 2x)| - 3) - 2 between the vertical lines x = 0.1 and x = 0.8. 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": "Calculate the area enclosed between the functions f(x) = -1|(1(-3sin(3\u03c0((3x + 1)/(-1x - 2))) + 1)^2 + 1(-3sin(3\u03c0((3x + 1)/(-1x - 2))) + 1)) - 1| - 2 and g(x) = -1(-3|((-2x - 3)/(2x - 1))| + 2) - 5 from x = -2.3 to x = -2.1999999999999997. 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) = -1cos(2\u03c0((1(1|(4x + 5) - 1| - 2) + 2)/(3(1|(4x + 5) - 1| - 2) + 2)) - 1) - 2, g(x) = (2(1(-4x - 2)^2 + 3(-4x - 2)) + 1)/(2(1(-4x - 2)^2 + 3(-4x - 2)) - 3), x = -0.6, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1|((1(2x + 1))/(-2(2x + 1) + 3)) - 3| + 2)^2 - 3(-1|((1(2x + 1))/(-2(2x + 1) + 3)) - 3| + 2) - 3 and g(x) = 1cos(2\u03c0(-4(1x^2 + 2x + 5) - 5) - 1) - 2 between the vertical lines x = -0.0 and 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": "Calculate the area enclosed between the functions f(x) = 1|(-1sin(2\u03c0((-3(4x^2 + 4x - 3) + 2)/(1(4x^2 + 4x - 3)))) - 2) + 3| - 2 and g(x) = 4(3|(2x^2 + 5x - 1) - 1| - 1) - 2 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2sin(3\u03c0(5((-3x)/(-3x - 3))^2) + 3) - 3 and g(x) = -2|((-1x - 2)/(-2x + 1))| - 3 from x = -2.3 to x = -2.1999999999999997. 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(2sin(1\u03c0(1|x - 3| + 1) + 2) - 3) + 4 and g(x) = 3|(5x^2 + 4x + 5) - 2| - 2 between the vertical lines x = -1.1 and x = -0.0. 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) = -1(4((-2(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 3))^2 - 1((-2(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 3)) - 3) - 1 and g(x) = (3(5(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) + 1) + 3)/(-1(5(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) + 1) - 1) between the vertical lines x = -0.2 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(2\u03c0(4(2|x + 2| + 3) + 4) + 1) and g(x) = (-1(-3|x + 3| - 1) + 3)/(-2(-3|x + 3| - 1) + 1) from x = 0.2 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) = -4(1sin(2\u03c0((2x - 1)/(-3x + 4)) + 3) - 1)^2 - 4(1sin(2\u03c0((2x - 1)/(-3x + 4)) + 3) - 1) - 1 and g(x) = (-2(1|x - 2| + 3) + 1)/(1(1|x - 2| + 3)) 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": "Calculate the area enclosed between the functions f(x) = 3|(3e^(1(3(1x^2 - 3x - 1) + 2)) + 3) - 3| + 1 and g(x) = 4(-2e^(-2(2x - 4)) + 1)^2 - 3(-2e^(-2(2x - 4)) + 1) + 1 from x = 2.6 to x = 2.8. 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) = 2(-2cos(1\u03c0(5x + 2)) + 3)^2 - 2(-2cos(1\u03c0(5x + 2)) + 3) + 4 and g(x) = 1(-1|x + 1| - 3)^2 + 5(-1|x + 1| - 3) - 4 from x = 2.9 to x = 3.1. 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": "Find the area of the region bounded by the curves f(x) = (1(4(-4(3|x + 2| + 2)^2 - 3(3|x + 2| + 2) - 5) - 2) + 2)/(1(4(-4(3|x + 2| + 2)^2 - 3(3|x + 2| + 2) - 5) - 2) + 3), g(x) = 1|(-3(1x^2 - 5x - 2) - 4)| - 2, x = 0.1, 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": "57.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(1e^(-1(5x - 5)) + 3)^2 - 4(1e^(-1(5x - 5)) + 3) - 5 and g(x) = -2cos(1\u03c0(5x - 3) + 2) from x = 3.4 to x = 3.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = -1((-2(2(1|x - 2| - 3)^2 + 1(1|x - 2| - 3) - 1) + 2)/(-3(2(1|x - 2| - 3)^2 + 1(1|x - 2| - 3) - 1) - 1)) + 2 and g(x) = 2sin(2\u03c0(3((2x - 1)/(1x + 2))^2 + 4((2x - 1)/(1x + 2)) - 2) + 3) + 3 between the vertical lines x = -4.0 and x = -3.9. 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) = 1((-3(-2e^(-1(2|x - 1| - 1)) - 1) - 1)/(3(-2e^(-1(2|x - 1| - 1)) - 1) + 2))^2 + 2((-3(-2e^(-1(2|x - 1| - 1)) - 1) - 1)/(3(-2e^(-1(2|x - 1| - 1)) - 1) + 2)) - 3, g(x) = 3(-2|((3x)/(3x + 1)) - 3| + 1)^2 + 2(-2|((3x)/(3x + 1)) - 3| + 1) - 5, x = -0.5, 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2((3(3|x + 3| - 1) - 1)/(2(3|x + 3| - 1) - 1))^2 + 1((3(3|x + 3| - 1) - 1)/(2(3|x + 3| - 1) - 1)) - 4) + 5, g(x) = 2(2|(-5x + 4) - 1| - 3)^2 - 2(2|(-5x + 4) - 1| - 3) - 4, x = 0.8, 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|((3(-3x^2 - 5x - 3) + 1)/(2(-3x^2 - 5x - 3) + 3)) - 2| - 2 and g(x) = 2|((-3x + 3)/(3x + 2)) + 1| + 1 between the vertical lines x = -1.5 and x = -1.0. 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) = (-3(-2|(-1(4x^2 + 5x - 1) - 3)|) + 3)/(1(-2|(-1(4x^2 + 5x - 1) - 3)|) + 3) and g(x) = 3sin(1\u03c0(-5((-3x - 2)/(1x + 3))^2 + 4((-3x - 2)/(1x + 3)) + 3) + 1) + 3 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": "Find the area of the region bounded by the curves f(x) = -2|(1(4((-3x - 2)/(3x + 3))^2 - 2((-3x - 2)/(3x + 3)) - 5) - 5) + 1| - 3, g(x) = -4(4(-1|x - 1| + 1)^2 + 5(-1|x - 1| + 1) - 4) - 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(2(2|x + 2| - 1) - 2))/(-3(2(2|x + 2| - 1) - 2) + 2), g(x) = 2|(-2e^(2x) - 2) - 3| + 3, x = -3.2, 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": "41.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(3\u03c0(-5(-3x - 3)^2 + 2(-3x - 3) + 5) + 1) - 2 and g(x) = 1((1x + 3)/(-2x + 1)) + 5 from x = 0.7 to x = 0.7999999999999999. 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(4(-2cos(3\u03c0x - 3) - 1) - 1)^2 - 2(4(-2cos(3\u03c0x - 3) - 1) - 1) - 3, g(x) = 3((-1x - 3)/(-2x + 3)) - 4, x = 1.6, 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": "22.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(-2((2x)/(-2x))^2 + 1((2x)/(-2x)) - 3) + 1) - 1 and g(x) = -2cos(2\u03c0(-2x - 5) - 3) - 2 between the vertical lines x = -2.7 and x = -2.3. 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) = -2|((-1(-1x + 2) - 3)/(1(-1x + 2))) + 3| + 2, g(x) = 1e^(1(-3x - 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(5(3|x - 1| - 1) + 1) + 3)/(-3(5(3|x - 1| - 1) + 1) + 4), g(x) = -1(-2x + 4)^2 + 2(-2x + 4) - 1, x = 0.6, 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": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(1e^(-1(-1x + 4))) + 3| - 2 and g(x) = 5(-2x^2 - 4x) between the vertical lines x = -2.4 and x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((-3(4(-2sin(1\u03c0x - 2) - 2) - 4) - 3)/(2(4(-2sin(1\u03c0x - 2) - 2) - 4) + 3)) - 1| - 2, g(x) = 5((3(3x - 3) - 1)/(-1(3x - 3) - 3))^2 + 2((3(3x - 3) - 1)/(-1(3x - 3) - 3)) - 3, x = 0.8, 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": "4.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((1(1e^(1(1|x - 1| + 2)) - 2))/(-1(1e^(1(1|x - 1| + 2)) - 2) - 1)) - 4, g(x) = (1(4(-3x^2 + 1x - 3) + 5) + 2)/(-2(4(-3x^2 + 1x - 3) + 5)), x = 0.6, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1e^(-2(2|(-5x - 2) - 3| + 3)) + 1 and g(x) = -3sin(2\u03c0(4x^2 + 3x + 4) - 1) - 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-3(1|x| - 2)^2 + 3) + 2)/(1(-3(1|x| - 2)^2 + 3) + 3) and g(x) = -1(-2e^(1x) + 3)^2 - 4(-2e^(1x) + 3) from x = -3.4 to x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-4(-3|x| - 1)^2 - 4(-3|x| - 1) - 2) + 3)/(1(-4(-3|x| - 1)^2 - 4(-3|x| - 1) - 2) - 3) and g(x) = (-3(-1|x - 3| - 1) + 3)/(1(-1|x - 3| - 1) - 3) from x = 1.2 to x = 5.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = 1|(2cos(2\u03c0(5x^2 - 5x + 3) - 1) + 1)| - 2 and g(x) = -2(-2sin(1\u03c0x) - 3)^2 - 5(-2sin(1\u03c0x) - 3) + 4 between the vertical lines x = 1.0 and x = 2.0. 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": "Find the area of the region bounded by the curves f(x) = -3(3|((1x - 3)/(-3x + 2)) - 3| - 3)^2 - 4(3|((1x - 3)/(-3x + 2)) - 3| - 3) + 2, g(x) = -4(-1x + 3)^2 - 2(-1x + 3) + 4, x = 0.8, 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": "4.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4((2(-3cos(2\u03c0x + 2) + 1) - 1)/(2(-3cos(2\u03c0x + 2) + 1) + 3)) - 3 and g(x) = 3|((-2x - 3)/(1x - 2)) + 2| - 1 from x = 1.6 to x = 1.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-5(2|x + 1| + 1) + 5) + 1)/(3(-5(2|x + 1| + 1) + 5)) and g(x) = -3((-1x + 1)/(2x - 1)) - 5 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-5(-2e^(-2x) + 2) - 2)^2 - 2(-5(-2e^(-2x) + 2) - 2) - 5, g(x) = 4(-1cos(3\u03c0x - 1) + 3) - 5, 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1cos(1\u03c0(2|(-5x^2 + 5) + 1| + 1)) + 2) - 1)/(1(-1cos(1\u03c0(2|(-5x^2 + 5) + 1| + 1)) + 2)) and g(x) = (3(4(2|x + 2| - 3)))/(2(4(2|x + 2| - 3)) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-1|(-4x^2 - 1) + 3| + 2) - 2 and g(x) = -4(1|x + 1| - 2)^2 - 4(1|x + 1| - 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(3|(1e^(-2x) - 2) - 3| + 2)^2 - 3(3|(1e^(-2x) - 2) - 3| + 2) - 2, g(x) = 2|((1x + 3)/(2x + 2)) - 2| - 1, 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": "46.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(3(1|(-2sin(1\u03c0x)) - 2| + 2)^2 + 4(1|(-2sin(1\u03c0x)) - 2| + 2)) + 3)/(-3(3(1|(-2sin(1\u03c0x)) - 2| + 2)^2 + 4(1|(-2sin(1\u03c0x)) - 2| + 2))) and g(x) = 2sin(3\u03c0(1|(1x^2 + 3x) + 1| + 2) - 3) + 1 from x = 3.7 to x = 3.8000000000000003. 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((-1(-2|x + 2| + 3) + 2)/(1(-2|x + 2| + 3) + 2))^2 - 3((-1(-2|x + 2| + 3) + 2)/(1(-2|x + 2| + 3) + 2)) + 1, g(x) = -2cos(3\u03c0((3x + 2)/(-1x - 3)) - 2) + 3, x = -2.3, and x = -2.1999999999999997. 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|(1(-5x^2 - 4x - 2) + 5) + 2| - 3 and g(x) = 1(1|x - 2| - 1)^2 - 5(1|x - 2| - 1) + 1 from x = -1.6 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((1(-2x + 5) + 2)/(-1(-2x + 5) - 3))^2 + 5((1(-2x + 5) + 2)/(-1(-2x + 5) - 3)) + 2 and g(x) = -2e^(-1(5x^2 + 5x - 4)) + 1 from x = 0.4 to x = 3.4. 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(2|(-3(3x + 4)^2 - 4(3x + 4) + 2) - 1| - 2) - 2)/(-2(2|(-3(3x + 4)^2 - 4(3x + 4) + 2) - 1| - 2) + 3) and g(x) = 1|(-4((1x + 3)/(3x + 2)) + 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": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(2|((-1x - 1)/(-2x - 3)) + 1| - 2) + 1, g(x) = (-2(1|x + 1| + 2) + 3)/(3(1|x + 1| + 2) + 2), x = -1.4, 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(5(2x^2 + 4x) - 1) + 1| + 1 and g(x) = (-2(-3x^2 - 4x - 1) + 2)/(-1(-3x^2 - 4x - 1) + 2) between the vertical lines x = -2.0 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": "Find the area of the region bounded by the curves f(x) = -1|((-2(-1x^2 - 4) + 2)/(-1(-1x^2 - 4) - 3)) + 1| + 2, g(x) = 1cos(2\u03c0(3x - 4)) - 1, x = 4.2, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((3(5x^2 - 3x + 3) + 3)/(1(5x^2 - 3x + 3) + 3)) + 4 and g(x) = (-1(-4x^2 + 1x + 1) - 3)/(-1(-4x^2 + 1x + 1) - 1) from x = -0.6 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(-1((-1(2x^2 - 4x - 4) + 1)/(3(2x^2 - 4x - 4) - 2))) + 1, g(x) = -3(-3e^(-2x) + 3)^2 - 5(-3e^(-2x) + 3) - 1, x = -0.2, 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": "Calculate the area enclosed between the functions f(x) = 2(3e^(1(-2x^2 - 5x - 2)) + 1) - 1 and g(x) = 4(-1sin(1\u03c0x + 3)) - 2 from x = 0.8 to x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-1sin(2\u03c0(3|((-2x - 3)/(-1x)) + 2| + 2) - 3) + 2)^2 + 2(-1sin(2\u03c0(3|((-2x - 3)/(-1x)) + 2| + 2) - 3) + 2) - 2 and g(x) = (-3(2|(-4x + 3) - 2| - 1) + 1)/(-2(2|(-4x + 3) - 2| - 1) - 1) from x = -0.3 to x = -0.19999999999999998. 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) = 1|(-3(3((-1x)/(-1x + 2))^2 + 4((-1x)/(-1x + 2)) + 3) + 3) + 3| and g(x) = (2(-3|(2x^2 - 5x + 3)| - 3) - 3)/(3(-3|(2x^2 - 5x + 3)| - 3) + 3) from x = 0.3 to x = 1.1. 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) = -3cos(3\u03c0((-2(1|(1x^2 + 2x + 5) - 3| - 2) - 1)/(-2(1|(1x^2 + 2x + 5) - 3| - 2) + 1)) - 2) + 3, g(x) = (1(-3|(-2x^2 + 1x + 2)| + 3) - 1)/(3(-3|(-2x^2 + 1x + 2)| + 3) + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(2cos(2\u03c0((-1x + 3)/(-3x + 1))) - 3) - 1| - 2, g(x) = 2|(3e^(-2x) - 2) - 1| + 1, x = 0.1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2e^(-1(-1|((-1x + 1)/(2x - 3))| + 3)) - 3 and g(x) = -2(-3sin(3\u03c0x + 1) - 1)^2 + 3(-3sin(3\u03c0x + 1) - 1) + 4 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(2(-1e^(1x) - 1) + 3) - 2)/(-2(2(-1e^(1x) - 1) + 3) + 1) and g(x) = -3e^(-1(-2|x - 2| + 3)) - 1 from x = -1.4 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(-1((2(2(1x^2 + 4x + 3) - 2) + 3)/(2(2(1x^2 + 4x + 3) - 2) + 3))) - 1 and g(x) = (2(-1(-2|x - 1| + 2) + 4) + 3)/(-2(-1(-2|x - 1| + 2) + 4) + 3) between the vertical lines x = -2.8 and x = 4.8. 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) = 1e^(-2(-1(2|(-1x^2 - 3x - 5) + 2| - 2) + 5)) + 3 and g(x) = 1((2(1cos(2\u03c0x + 3) + 1) - 3)/(1(1cos(2\u03c0x + 3) + 1) - 2)) + 2 between the vertical lines x = -1.2 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": "Calculate the area enclosed between the functions f(x) = 2|(-3e^(1(4((-2x - 3)/(-3x + 4))^2 - 1((-2x - 3)/(-3x + 4)))) - 3) - 1| + 2 and g(x) = 5(2sin(3\u03c0(-1|x|) - 3) - 2)^2 - 2(2sin(3\u03c0(-1|x|) - 3) - 2) + 5 from x = -2.3 to x = -2.0. Round 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) = 3cos(2\u03c0(4((-2x)/(3x + 3)) - 3) - 1) - 2, g(x) = -3|(3sin(3\u03c0x) + 3) - 2|, x = 4.7, and x = 5.0. 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) = -3cos(1\u03c0(-3|(-5x + 1) + 2| + 1) - 1), g(x) = -4((1x - 3)/(-3x - 2))^2 + 2((1x - 3)/(-3x - 2)) + 5, x = -3.1, 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(1(-2sin(1\u03c0x - 1) - 1)^2 - 3(-2sin(1\u03c0x - 1) - 1) - 3) + 3)/(2(1(-2sin(1\u03c0x - 1) - 1)^2 - 3(-2sin(1\u03c0x - 1) - 1) - 3) - 1) and g(x) = -2|((-1x - 1)/(1x + 2)) - 2| - 2 between the vertical lines x = 1.3 and x = 2.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2\u03c0(1(-4x - 4)^2 - 4(-4x - 4) - 2) - 2) - 2 and g(x) = -1(2x - 5)^2 + 3(2x - 5) - 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2|(-2sin(3\u03c0x - 1) - 3) + 1| + 2) + 1)/(3(2|(-2sin(3\u03c0x - 1) - 3) + 1| + 2) - 2), g(x) = -1((3x + 2)/(-1x)) - 1, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|(-4(-1((-2x - 3)/(-3x - 1))^2 + 2((-2x - 3)/(-3x - 1)) + 4) + 5) - 3| - 1 and g(x) = 4(2cos(2\u03c0(1x + 3) + 2) + 3)^2 - 4(2cos(2\u03c0(1x + 3) + 2) + 3) - 4 between the vertical lines x = 2.4 and x = 2.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0(-1(1x + 2)^2 + 2(1x + 2) + 3) + 3) + 1, g(x) = (1(-2e^(1x) - 3) + 2)/(-2(-2e^(1x) - 3)), x = -4.7, and x = -4.6000000000000005. 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) = -1cos(2\u03c0(4(-3(3|x - 2| - 1)^2 - 2(3|x - 2| - 1) - 3) - 1)) and g(x) = 2|(5(-1cos(3\u03c0x - 1) - 1)) + 2| - 1 between the vertical lines x = -3 and x = 3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1cos(2\u03c0(2x^2 - 5x + 1)) - 3) + 2)/(-2(-1cos(2\u03c0(2x^2 - 5x + 1)) - 3) - 2), g(x) = 5(3e^(-1x)) + 2, x = 4.8, and x = 4.8999999999999995. 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(-1(-3sin(1\u03c0((-1x + 1)/(-1x - 1)) + 1) + 1) - 3)^2 - 2(-1(-3sin(1\u03c0((-1x + 1)/(-1x - 1)) + 1) + 1) - 3), g(x) = (3(2|(-3x - 2) + 3| - 3) + 3)/(-2(2|(-3x - 2) + 3| - 3) + 1), x = -0.2, 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": "36.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1e^(1((-2x)/(-2x + 1))) + 1) - 5 and g(x) = (-2(2cos(2\u03c0x + 2)) - 3)/(-1(2cos(2\u03c0x + 2)) - 1) between the vertical lines x = -4.7 and x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(3cos(1\u03c0((2x - 2)/(2x)) - 1) - 2) and g(x) = (1(-5x^2 - 1) + 2)/(1(-5x^2 - 1) - 2) 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(2cos(1\u03c0(-2|x + 3|) - 3) - 1)^2 + 4(2cos(1\u03c0(-2|x + 3|) - 3) - 1) - 4, g(x) = 2|(2x^2 - 1x + 5)| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2(2x^2 + 2x - 2) - 1) + 3)/(3(-2(2x^2 + 2x - 2) - 1) + 2), g(x) = 1(5x - 5)^2 + 5(5x - 5) + 5, 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": "74.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(2|(3x - 3) - 2| - 3))/(-1(2|(3x - 3) - 2| - 3) - 2) and g(x) = -2sin(1\u03c0((-1x - 2)/(1x + 1)) + 2) from x = 1.3 to x = 2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(1(-3(-3|x + 3|) - 5)^2 + 5(-3(-3|x + 3|) - 5) - 4) + 2)/(2(1(-3(-3|x + 3|) - 5)^2 + 5(-3(-3|x + 3|) - 5) - 4) + 2) and g(x) = (1(-2|(3x - 1) - 3|) + 2)/(2(-2|(3x - 1) - 3|) - 1) from x = -3.6 to x = -2.4. 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) = 1|(1(2((2x + 1)/(1x - 3))^2 - 4((2x + 1)/(1x - 3)) + 2) - 1) - 3| - 2 and g(x) = 2|(1e^(2(3x - 2))) - 3| + 1 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) = 2|(2e^(2(-4(1x^2 - 5x + 1) + 5)) - 3) - 3| + 3, g(x) = 3((-3(1x + 1))/(-1(1x + 1) + 2))^2 + 2((-3(1x + 1))/(-1(1x + 1) + 2)), 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(2\u03c0((-2(1|x + 3| + 1) - 3)/(-2(1|x + 3| + 1) + 3)) - 3) - 3 and g(x) = -1|(-1e^(-1x) + 2) - 2| - 3 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1(1(3|x - 3| + 1) + 1)^2 + 4(1(3|x - 3| + 1) + 1) + 5) - 2)/(1(-1(1(3|x - 3| + 1) + 1)^2 + 4(1(3|x - 3| + 1) + 1) + 5)), g(x) = (-1(4(3cos(1\u03c0x + 1) - 1)^2 - 2))/(-3(4(3cos(1\u03c0x + 1) - 1)^2 - 2) + 4), x = -2.8, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-1|(-5(4x^2 - 4x + 5) - 2) - 1| + 3) + 3)/(1(-1|(-5(4x^2 - 4x + 5) - 2) - 1| + 3) + 3), g(x) = 2|((-1(5x^2 - 4x - 3) - 3)/(-2(5x^2 - 4x - 3) + 3)) + 2| - 3, 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": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(1|x - 3| + 2)^2 + 5(1|x - 3| + 2) + 5) + 1)/(3(1(1|x - 3| + 2)^2 + 5(1|x - 3| + 2) + 5) + 3) and g(x) = (1(-3|x - 2| + 2) + 3)/(3(-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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(-1(-1|(-4x^2 + 1x - 1) + 2| + 2)) - 2, g(x) = -3e^(2(-5x^2 - 1x - 1)) + 2, x = -0.8, 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": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-5(3|(-3x - 5) - 1| + 1)^2 + 4(3|(-3x - 5) - 1| + 1) - 4) - 1)/(2(-5(3|(-3x - 5) - 1| + 1)^2 + 4(3|(-3x - 5) - 1| + 1) - 4) + 2), g(x) = 1sin(2\u03c0(-2((-3x - 2)/(1x + 1)) + 4) + 1) - 1, x = -1.0, 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": "Find the area of the region bounded by the curves f(x) = 1cos(3\u03c0((1(5(-3x^2 - 1x + 1) + 2) + 3)/(-2(5(-3x^2 - 1x + 1) + 2) - 2)) + 3) - 2, g(x) = 1(1|(3x - 4) + 3| - 1)^2 - 2(1|(3x - 4) + 3| - 1) - 1, x = 0.7, 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": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3|(3sin(1\u03c0x - 1) - 1) + 3| + 1) - 1 and g(x) = 2e^(-1(1x + 5)) - 2 between the vertical lines x = -4.0 and x = -3.9. 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) = 1((1(2|(-3x^2 - 4x + 4) - 2|) + 3)/(3(2|(-3x^2 - 4x + 4) - 2|) - 1)) + 4, g(x) = -4(4((3x + 1)/(-2x + 1))^2 - 1((3x + 1)/(-2x + 1)) + 2) + 1, x = -1.7, and x = -1.5999999999999999. Round your answer to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(1\u03c0((-2(-2|x + 1| + 3) - 1)/(-3(-2|x + 1| + 3))) - 1) + 1, g(x) = 1|(-4x + 2) + 3| - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3e^(-2(-5x - 1)) + 1) + 2| - 2 and g(x) = (-1(-2|x + 2| + 2) + 3)/(1(-2|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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (1(-5(3(2cos(1\u03c0x + 3) - 3)^2 + 2(2cos(1\u03c0x + 3) - 3) + 1) - 2) - 3)/(-1(-5(3(2cos(1\u03c0x + 3) - 3)^2 + 2(2cos(1\u03c0x + 3) - 3) + 1) - 2) - 2), g(x) = 2cos(1\u03c0(2|(3x^2 + 5x + 1) - 1| + 2)) - 2, x = 4.0, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-2cos(3\u03c0(2(-2|x + 3| + 2) - 2) + 2) - 1)^2 - 4(-2cos(3\u03c0(2(-2|x + 3| + 2) - 2) + 2) - 1) - 2 and g(x) = (2(1(-1|x| + 2) - 1) - 1)/(-3(1(-1|x| + 2) - 1) + 4) from x = -2.6 to x = -2.5. 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) = -2(-2cos(2\u03c0(1|x + 3| + 3) + 2) - 3) - 5, g(x) = 2|(3x^2 - 4x - 5) + 2| + 1, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-1(3cos(2\u03c0((1x + 2)/(-3x - 2)) + 1) + 3) + 1)^2 - 1 and g(x) = -5((-2(-2|x + 3| + 2) + 2)/(-2(-2|x + 3| + 2) + 1))^2 - 4((-2(-2|x + 3| + 2) + 2)/(-2(-2|x + 3| + 2) + 1)) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-2(-4(-1|x + 2| - 2) - 1)^2 + 4(-4(-1|x + 2| - 2) - 1) - 2))/(3(-2(-4(-1|x + 2| - 2) - 1)^2 + 4(-4(-1|x + 2| - 2) - 1) - 2) - 1), g(x) = -2(2((3x + 1)/(-2x - 2))^2 - 4((3x + 1)/(-2x - 2)) + 3) + 3, x = -0.7, 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": "Find the area of the region bounded by the curves f(x) = 2|(2e^(-1(-1x + 4)) - 3) - 1| + 3, g(x) = 3|(2x + 5)| - 1, x = -4.5, 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": "24.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(3sin(2\u03c0(5(-5x^2 - 2x - 4) - 2)) - 2) - 1| + 2 and g(x) = (1(-3|(-1sin(2\u03c0x - 3) + 3) - 1| + 1) - 2)/(-1(-3|(-1sin(2\u03c0x - 3) + 3) - 1| + 1) - 3) 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": "4.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2cos(3\u03c0(-1|x - 1|) + 3) - 2) + 1 and g(x) = 2sin(2\u03c0(-2x^2 + 5x + 4) + 2) + 2 between the vertical lines x = -5.0 and x = -4.9. 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) = 2(1(1|((2x + 3)/(-1x + 3))|)^2 + 1) - 3, g(x) = -2|(4((-3x - 3)/(-1x + 2))^2 + 1((-3x - 3)/(-1x + 2)) - 5) + 1|, x = -2.4, 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": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2|(2x - 4) + 1| + 2)^2 - 5(-2|(2x - 4) + 1| + 2) and g(x) = 2cos(1\u03c0((-1x - 1)/(-2x - 1)) - 3) + 3 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": "1.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(2cos(1\u03c0(1x^2 - 3x + 5) - 1) - 3) - 2)/(-3(2cos(1\u03c0(1x^2 - 3x + 5) - 1) - 3) - 3) and g(x) = 4(2x + 4)^2 + 5(2x + 4) + 2 between the vertical lines x = -2.4 and x = -2.2. 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) = 5(5((-1x + 1)/(1x + 1))^2 + 2((-1x + 1)/(1x + 1)) + 3) and g(x) = 3(1|x| + 2)^2 + 4(1|x| + 2) - 5 from x = -3.1 to x = 0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-142.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((2(-1x^2 - 1x - 4) - 1)/(-2(-1x^2 - 1x - 4) - 2)) - 3| + 1 and g(x) = -3(-2sin(3\u03c0x - 2) + 2)^2 + 5 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": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2((3(1(3|x - 1| + 1)^2 + 5(3|x - 1| + 1) - 5) + 1)/(2(1(3|x - 1| + 1)^2 + 5(3|x - 1| + 1) - 5) + 1)) - 1 and g(x) = (3(-3sin(3\u03c0(1x + 4) + 1) + 1) + 1)/(-2(-3sin(3\u03c0(1x + 4) + 1) + 1) - 3) between the vertical lines x = -0.0 and x = 0.2. 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": "Determine the area of the region enclosed by the graphs of f(x) = -4((1(-3|(2x^2 + 3x + 2) - 3| + 2) + 1)/(-3(-3|(2x^2 + 3x + 2) - 3| + 2))) - 4 and g(x) = (-1(1|(4x^2 + 3x + 4) - 3| + 1) + 1)/(1(1|(4x^2 + 3x + 4) - 3| + 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-5(3|x + 2| + 3) + 2) + 1)/(-1(-5(3|x + 2| + 3) + 2) + 3) and g(x) = -1|(-4x + 1) - 3| + 3 between the vertical lines x = -1.0 and x = 0.0. 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": "Calculate the area enclosed between the functions f(x) = (-1(-2|(-1x^2 + 3x + 2) + 3| + 1))/(3(-2|(-1x^2 + 3x + 2) + 3| + 1) - 1) and g(x) = -1(-4x^2 + 4x) from x = -1.1 to x = 0.1. 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": "Find the area of the region bounded by the curves f(x) = 1(-1((-3(-2|x| - 1) + 3)/(-2(-2|x| - 1) - 2))^2 + 3((-3(-2|x| - 1) + 3)/(-2(-2|x| - 1) - 2)) - 2) + 5, g(x) = -1(-2|(-4x + 5) + 3| + 3)^2 - 5(-2|(-4x + 5) + 3| + 3) - 2, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-1(1|(4x^2 + 4) - 3| + 1) + 3) - 3)/(-3(-1(1|(4x^2 + 4) - 3| + 1) + 3) + 4), g(x) = (3(-3cos(1\u03c0(2|x|) - 1) + 1) + 1)/(3(-3cos(1\u03c0(2|x|) - 1) + 1) - 1), x = 4.4, and x = 5.0. 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) = -4((-3(1x + 1) - 3)/(3(1x + 1) + 1))^2 - 3((-3(1x + 1) - 3)/(3(1x + 1) + 1)) + 5 and g(x) = 1((2x - 2)/(-1x + 2))^2 - 4((2x - 2)/(-1x + 2)) + 4 between the vertical lines x = 1.2 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((3(-4(1x + 1)^2 + 1(1x + 1) + 2) + 2)/(1(-4(1x + 1)^2 + 1(1x + 1) + 2))) + 2| + 1, g(x) = -2((3(3sin(1\u03c0x + 1)) - 3)/(3(3sin(1\u03c0x + 1)))) - 4, x = -0.3, 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": "29.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1|(-3e^(2x) - 2)| - 2) + 1)/(-2(-1|(-3e^(2x) - 2)| - 2) + 3) and g(x) = (-3(-3|x - 2|) + 1)/(2(-3|x - 2|) - 3) between the vertical lines x = 1.9 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": "Calculate the area enclosed between the functions f(x) = (3(-2(-2cos(3\u03c0x - 2))^2 + 1(-2cos(3\u03c0x - 2))) + 2)/(-1(-2(-2cos(3\u03c0x - 2))^2 + 1(-2cos(3\u03c0x - 2))) - 3) and g(x) = 1(2x + 3)^2 + 1(2x + 3) 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": "6.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(4(2sin(1\u03c0(-4x - 4) + 1) + 1)^2 - 4(2sin(1\u03c0(-4x - 4) + 1) + 1) - 1) + 1)/(2(4(2sin(1\u03c0(-4x - 4) + 1) + 1)^2 - 4(2sin(1\u03c0(-4x - 4) + 1) + 1) - 1) + 2), g(x) = -4((-3(2cos(1\u03c0x + 1) - 1) - 1)/(3(2cos(1\u03c0x + 1) - 1))) + 3, 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(2cos(2\u03c0(4x - 5) - 3) + 2) + 2)/(1(2cos(2\u03c0(4x - 5) - 3) + 2) + 2) and g(x) = (1(-1x + 2) - 3)/(3(-1x + 2) + 1) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3(1cos(2\u03c0(1x + 2) - 3) + 3)^2 + 1(1cos(2\u03c0(1x + 2) - 3) + 3) + 1, g(x) = 5(4x + 5)^2 - 2(4x + 5) - 5, x = -1.8, 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": "38.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1cos(1\u03c0(-2(1|x + 2| - 3)^2 - 1(1|x + 2| - 3)) - 3) and g(x) = -3|((2x - 2)/(3x + 3)) - 3| + 3 from x = -2.2 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": "Find the area of the region bounded by the curves f(x) = 2|(4((-2(-2x^2 - 1x - 4) - 1)/(3(-2x^2 - 1x - 4) - 2)) - 3) - 1| - 3, g(x) = (1(-2cos(1\u03c0(5x^2 + 1x - 5) - 3) - 2) - 3)/(1(-2cos(1\u03c0(5x^2 + 1x - 5) - 3) - 2) + 1), x = -1.9, 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(-1|(-3(3cos(2\u03c0x - 3) - 1) - 4) + 3| + 1))/(2(-1|(-3(3cos(2\u03c0x - 3) - 1) - 4) + 3| + 1) + 1) and g(x) = 1cos(3\u03c0(2(1|x + 3| - 1) + 4) - 1) + 1 between the vertical lines x = 4.3 and x = 4.3999999999999995. 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) = -4((2(-1(1|x + 1| - 2)^2 + 3(1|x + 1| - 2) + 4) + 2)/(1(-1(1|x + 1| - 2)^2 + 3(1|x + 1| - 2) + 4) + 3)) + 3 and g(x) = -1sin(1\u03c0((-1(4x^2 + 4x + 1) + 2)/(-1(4x^2 + 4x + 1))) + 3) - 3 from x = 0.5 to x = 3.9. 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(4(-1sin(3\u03c0x - 1) + 2)^2 + 5(-1sin(3\u03c0x - 1) + 2) - 5) - 1)/(2(4(-1sin(3\u03c0x - 1) + 2)^2 + 5(-1sin(3\u03c0x - 1) + 2) - 5) + 1) and g(x) = (-3(-1sin(1\u03c0x - 3)) - 1)/(2(-1sin(1\u03c0x - 3)) - 1) between the vertical lines x = 1.9 and x = 3.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2(2cos(2\u03c0x + 3) + 1)^2 - 2(2cos(2\u03c0x + 3) + 1) - 5) + 1, g(x) = -2cos(3\u03c0(2x^2 - 3x + 4) + 3) + 1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(3((1x - 1)/(2x + 2)) - 1)^2 + 3(3((1x - 1)/(2x + 2)) - 1) and g(x) = -1|(-2x^2) - 3| - 2 from x = -2.5 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-74.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(4(3sin(3\u03c0(4x^2 - 1x - 4) + 1) + 1) + 5) - 3)/(-3(4(3sin(3\u03c0(4x^2 - 1x - 4) + 1) + 1) + 5) + 4) and g(x) = -3|((1(-5x))/(3(-5x) + 1)) - 3| from x = 3.0 to x = 3.1. 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) = 5((3(1|(-3cos(1\u03c0x + 1) - 3) + 2| + 2))/(2(1|(-3cos(1\u03c0x + 1) - 3) + 2| + 2) + 3)) - 4 and g(x) = 1(3e^(1(2x^2 - 4x - 3)) - 3) - 1 from x = -0.7 to x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1((-1(-2|x + 2| + 3) + 1)/(1(-2|x + 2| + 3) - 2)) + 3, g(x) = 1cos(2\u03c0(4x^2 - 5x + 5) - 1) + 2, x = 4.2, and x = 4.3. 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) = -1cos(2\u03c0((-3(3(1|x|) + 5) + 3)/(-2(3(1|x|) + 5) - 2)) + 1) + 1 and g(x) = 5(-2(1cos(3\u03c0x - 3) - 2) - 4)^2 + 4(-2(1cos(3\u03c0x - 3) - 2) - 4) + 2 between the vertical lines x = -1.5 and x = -1.2. 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) = 3|(-1cos(1\u03c0(2(3x^2 - 3x - 3) - 1) + 1) - 1) + 2| + 3 and g(x) = 1|(-4(3cos(3\u03c0x + 1) - 1) + 2) - 1| + 2 between the vertical lines x = -2.3 and x = -2.2. 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) = -4((-3(-2|x - 3| + 3) + 1)/(1(-2|x - 3| + 3) + 1))^2 - 5((-3(-2|x - 3| + 3) + 1)/(1(-2|x - 3| + 3) + 1)) - 4 and g(x) = (3(-3x - 5) - 2)/(-1(-3x - 5) - 1) between the vertical lines x = 4.0 and x = 4.3. 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) = (-3(-1(-2(-1|x - 3| + 3) - 3)^2 + 4(-2(-1|x - 3| + 3) - 3) - 1))/(-3(-1(-2(-1|x - 3| + 3) - 3)^2 + 4(-2(-1|x - 3| + 3) - 3) - 1) - 2) and g(x) = -1sin(3\u03c0((3(-5x - 1))/(-3(-5x - 1) - 1)) - 1) between the vertical lines x = -3.4 and 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) = -4(2sin(1\u03c0(-2|(-4x^2 - 2x - 5)| - 3) - 2) - 1) - 1 and g(x) = (-3(5(3|x - 1| + 2)^2 + 1(3|x - 1| + 2)))/(-2(5(3|x - 1| + 2)^2 + 1(3|x - 1| + 2)) - 2) 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(1(-3|(1x^2 + 5x) - 3| + 3)) - 1)/(-1(1(-3|(1x^2 + 5x) - 3| + 3)) - 3) and g(x) = -2(-1((2x + 3)/(-2x - 1))^2 - 1) + 4 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(2e^(-2(1|x + 3| - 3)) + 3) + 1 and g(x) = (-3(-3x^2 + 3x + 1) + 3)/(1(-3x^2 + 3x + 1) - 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) = -5((3(2|(5x - 3) + 2| - 3) - 1)/(1(2|(5x - 3) + 2| - 3) - 3))^2 - 2((3(2|(5x - 3) + 2| - 3) - 1)/(1(2|(5x - 3) + 2| - 3) - 3)) - 4 and g(x) = 5(2|(1sin(3\u03c0x + 1)) + 1| - 3) between the vertical lines x = -0.1 and x = 0.4. 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) = 1(-1|((-1(-2x - 5) - 3)/(-1(-2x - 5) + 3)) + 1| - 1)^2 - 1(-1|((-1(-2x - 5) - 3)/(-1(-2x - 5) + 3)) + 1| - 1) - 4 and g(x) = 2e^(1(4(1|x + 1| - 2) - 1)) + 1 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3e^(-1(3|(-1x^2 + 5x - 4) + 1| - 1)) + 3, g(x) = 1|(3sin(3\u03c0x + 1) + 3) - 3| + 1, 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": "Determine the area of the region enclosed by the graphs of f(x) = -3(-2((-1(-2|x - 1| + 1) - 3)/(2(-2|x - 1| + 1) + 3))^2 - 5((-1(-2|x - 1| + 1) - 3)/(2(-2|x - 1| + 1) + 3)) + 3) + 3 and g(x) = -3(2cos(1\u03c0(-1x + 5) - 1) + 2)^2 - 2(2cos(1\u03c0(-1x + 5) - 1) + 2) + 4 between the vertical lines x = 3.2 and x = 4.2. 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": "Determine the area of the region enclosed by the graphs of f(x) = 5((-2(-3|(-5x^2 - 2x + 3) - 1| - 2))/(-3(-3|(-5x^2 - 2x + 3) - 1| - 2) + 1)) + 4 and g(x) = -1(1sin(3\u03c0(-3x^2 + 2x - 4)) - 3) + 3 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(2\u03c0(4(3x^2 + 2) - 3) + 2) - 1 and g(x) = -2cos(2\u03c0(-1x + 4) + 1) + 2 between the vertical lines x = 2.1 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": "Find the area of the region bounded by the curves f(x) = (3(-3|(-3cos(3\u03c0x + 3) + 3) + 1| + 3))/(1(-3|(-3cos(3\u03c0x + 3) + 3) + 1| + 3) + 2), g(x) = (-1(1sin(1\u03c0x) + 1) + 2)/(1(1sin(1\u03c0x) + 1)), x = 1.6, 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": "14.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-2((-1(-1cos(2\u03c0x - 1) - 3) - 3)/(1(-1cos(2\u03c0x - 1) - 3) + 2))^2 - 3((-1(-1cos(2\u03c0x - 1) - 3) - 3)/(1(-1cos(2\u03c0x - 1) - 3) + 2)) + 4) - 4 and g(x) = -3((2(-3|x + 3| - 2) - 1)/(2(-3|x + 3| - 2) - 1)) + 5 between the vertical lines x = 0.8 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(2|((3(3x - 5) + 2)/(-1(3x - 5) + 3)) + 2| - 1)^2 - 5(2|((3(3x - 5) + 2)/(-1(3x - 5) + 3)) + 2| - 1) - 1 and g(x) = 1(1(1|x - 2| - 1)^2 - 1) between the vertical lines x = -1.5 and x = 0.1. 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) = (-3(-3(1|x + 2|)^2 - 4(1|x + 2|) + 3) - 2)/(-1(-3(1|x + 2|)^2 - 4(1|x + 2|) + 3) + 3) and g(x) = -5(-3cos(2\u03c0x - 2) + 3)^2 + 1(-3cos(2\u03c0x - 2) + 3) + 1 from x = -2.0 to x = -1.9. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(3|(3sin(3\u03c0x) + 1) - 1| - 1) + 2)/(-3(3|(3sin(3\u03c0x) + 1) - 1| - 1) - 2) and g(x) = (-3(2cos(1\u03c0x - 1) + 2) - 3)/(1(2cos(1\u03c0x - 1) + 2) - 3) between the vertical lines x = 0.3 and x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(3(-1|x - 1| + 2)^2 - 1(-1|x - 1| + 2) + 3) - 3)/(-2(3(-1|x - 1| + 2)^2 - 1(-1|x - 1| + 2) + 3) - 3) and g(x) = -3cos(1\u03c0(2|x + 3| + 1)) + 1 from x = 2.7 to 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": "Determine the area of the region enclosed by the graphs of f(x) = 2|(2cos(3\u03c0(5x^2 - 3x + 5) - 3) + 1)| - 3 and g(x) = -1(-2x^2 + 5x - 5) + 1 between the vertical lines x = 1.3 and x = 1.4. 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) = -1((-3(-1(-1|x| + 3)^2 - 2(-1|x| + 3) + 4) - 1)/(-1(-1(-1|x| + 3)^2 - 2(-1|x| + 3) + 4) + 3)), g(x) = 1sin(1\u03c0(1|(1x^2 - 1x - 1) + 3| - 1) - 3) + 1, x = -1.8, 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": "9.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-1(2sin(1\u03c0(-2x - 4) + 1) + 1) - 3)/(1(2sin(1\u03c0(-2x - 4) + 1) + 1)))^2 - 3((-1(2sin(1\u03c0(-2x - 4) + 1) + 1) - 3)/(1(2sin(1\u03c0(-2x - 4) + 1) + 1))) + 3, g(x) = 5(-2|(2x - 4) - 2| - 1)^2 + 3(-2|(2x - 4) - 2| - 1) - 5, x = 2.8, 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(2|((1x - 2)/(-1x + 3)) + 1| - 2) + 2, g(x) = 2(-2sin(3\u03c0x + 3) - 1)^2 + 5(-2sin(3\u03c0x + 3) - 1) - 5, 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) = -1|(-4(1e^(-2(-1x^2 - 5x - 3)) - 3) + 3) + 2| and g(x) = -1e^(2(-1|(-4x^2 - 1x - 4) + 3| + 2)) - 3 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3sin(1\u03c0(-4x^2 + 1x + 1) - 2) - 3) + 1| - 3 and g(x) = -3((-2x)/(-3x - 3)) - 2 from x = 1.6 to x = 1.7000000000000002. 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) = -4(2|(1sin(3\u03c0x + 1) - 1)| - 1) + 3, g(x) = -1e^(1((2x - 3)/(2x - 3))) + 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": "1.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1cos(2\u03c0(2|x + 3| + 3) - 2) + 1)^2 + 3(-1cos(2\u03c0(2|x + 3| + 3) - 2) + 1) + 4, g(x) = 3|(3x + 2) - 1| - 3, x = 1.0, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3cos(3\u03c0(1(3|x + 3| + 3) - 4)) + 3 and g(x) = (3(1x + 2) - 3)/(1(1x + 2) - 3) from x = 3.4 to x = 3.5. 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) = 1((2(-1(2|x + 2| - 2)^2 - 5(2|x + 2| - 2) - 2) + 3)/(3(-1(2|x + 2| - 2)^2 - 5(2|x + 2| - 2) - 2) + 2)) - 2 and g(x) = -3cos(1\u03c0(-2|((3x + 3)/(1x - 2)) - 1| + 1) + 1) + 3 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": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(-2(1((1x + 1)/(-1x + 2))^2 - 4((1x + 1)/(-1x + 2)) - 5) - 2) + 2|, g(x) = -1((2(-2|x - 2| - 3) - 3)/(2(-2|x - 2| - 3) - 1))^2 - 5((2(-2|x - 2| - 3) - 3)/(2(-2|x - 2| - 3) - 1)) - 3, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1sin(1\u03c0(-3(-1x^2 + 2x - 2) + 5) + 2) - 1, g(x) = (2(-3x - 1) + 1)/(-1(-3x - 1) - 1), x = -2.0, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(3\u03c0(-1((-2(2|x + 3| + 3) + 3)/(1(2|x + 3| + 3))) - 4) - 3) - 1 and g(x) = (2(-3|(1cos(2\u03c0x + 3) - 1) - 3|) + 1)/(-2(-3|(1cos(2\u03c0x + 3) - 1) - 3|) + 3) between the vertical lines x = -3.3 and x = -2.7. 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) = -1cos(2\u03c0((2(2x + 2) + 1)/(3(2x + 2) - 1)) + 2) - 3 and g(x) = -2|(1x^2 - 1x + 5) - 3| + 2 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4(1((3(3|x - 2| - 1) - 2)/(-1(3|x - 2| - 1) + 3))^2 - 3((3(3|x - 2| - 1) - 2)/(-1(3|x - 2| - 1) + 3)) - 2) + 5, g(x) = 1(-3|(-1x^2 + 1x + 2) + 2|) - 1, x = 2.5, 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5(-3|(1cos(1\u03c0x - 1))| - 1)^2 - 2(-3|(1cos(1\u03c0x - 1))| - 1), g(x) = 3cos(1\u03c0(1x^2 - 4x + 1) + 1) - 3, x = -4.2, and x = -4.1000000000000005. 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(-3(2|((2x + 1)/(3x - 2)) + 3| - 1) + 4)^2 and g(x) = -4(1((1x + 1)/(-2x - 2))^2 + 1((1x + 1)/(-2x - 2)) + 2) - 2 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(1(2|((-1x - 1)/(1x - 3)) + 3|) + 3)^2 - 2(1(2|((-1x - 1)/(1x - 3)) + 3|) + 3) - 1 and g(x) = -2((-3(-5x) - 2)/(3(-5x) - 1))^2 - 3((-3(-5x) - 2)/(3(-5x) - 1)) - 3 between the vertical lines x = -0.1 and x = -0.0. 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) = 5((-1(-1|(-3x^2 + 4x + 3) - 3| + 3))/(2(-1|(-3x^2 + 4x + 3) - 3| + 3) - 1)) - 3, g(x) = 2|(1(1cos(2\u03c0x - 3) - 2)^2 - 3(1cos(2\u03c0x - 3) - 2) - 5) + 1| - 2, x = -0.5, 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": "43.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(5(-1cos(3\u03c0(3|x + 3| - 1) + 2) - 2)^2 + 3(-1cos(3\u03c0(3|x + 3| - 1) + 2) - 2) + 1) + 2 and g(x) = 2(-2|(4x - 4) + 1| - 1)^2 + 5(-2|(4x - 4) + 1| - 1) - 5 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-1|(1(-3sin(3\u03c0x + 2) + 1) + 2) - 3| - 2)^2 - 5(-1|(1(-3sin(3\u03c0x + 2) + 1) + 2) - 3| - 2) + 3, g(x) = (-1(2(-1x^2 - 2x)) + 1)/(-2(2(-1x^2 - 2x)) - 2), x = -2.2, 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": "92.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-5((-2x - 3)/(-2x + 1))^2 - 3((-2x - 3)/(-2x + 1)) - 2) + 1 and g(x) = 3(3x^2 + 3x - 5) - 4 from x = -2.0 to x = -0.1. 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) = 5(-1((-2(-2cos(1\u03c0x) + 3) - 2)/(-1(-2cos(1\u03c0x) + 3)))^2 - 2((-2(-2cos(1\u03c0x) + 3) - 2)/(-1(-2cos(1\u03c0x) + 3))) - 5) + 2 and g(x) = (-1(-3|(1x + 3) - 3|) - 2)/(-2(-3|(1x + 3) - 3|) - 1) 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": "55.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(3(3|x + 1|)^2 - 2(3|x + 1|) - 5) + 4 and g(x) = (2(4x^2 - 4x + 4) - 2)/(-1(4x^2 - 4x + 4) + 3) from x = -0.2 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) = -1e^(2(5(2|x - 2| - 3)^2 + 5(2|x - 2| - 3) - 2)), g(x) = -1|(5x^2 + 1x + 2) + 2| - 1, x = 2.7, 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": "65.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-5(3|x - 2| - 1) - 3) + 3)/(-2(-5(3|x - 2| - 1) - 3) - 1), g(x) = -1|(-5x) + 2| - 2, x = 1.8, 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": "9.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(1|(1e^(-2x) - 1) - 1| - 1)^2 - 3 and g(x) = -1((3x - 2)/(2x))^2 - 4((3x - 2)/(2x)) - 2 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-1(-2(-3|x + 1|)^2 - 3(-3|x + 1|) - 1) + 1) + 1)/(2(-1(-2(-3|x + 1|)^2 - 3(-3|x + 1|) - 1) + 1) + 1) and g(x) = 2|(-2(-2x^2 + 4x - 1) - 3)| - 2 between the vertical lines x = -0.0 and x = 2.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1cos(2\u03c0(4((3x - 1)/(-1x - 2)) - 4) - 3) - 3)^2 - 4(-1cos(2\u03c0(4((3x - 1)/(-1x - 2)) - 4) - 3) - 3) and g(x) = -2(-4((-3x + 1)/(-2x))^2 - 4((-3x + 1)/(-2x)) + 4) + 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(-2((-2(4x^2 + 4x))/(3(4x^2 + 4x) - 1)) - 3) - 3| + 3, g(x) = -3sin(2\u03c0((-3(-1|x + 3| - 3) - 1)/(-2(-1|x + 3| - 3) - 3)) + 1) + 3, 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": "13.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(1|(-5(-1sin(2\u03c0x - 3)) + 4) - 2| - 2)^2 - 2(1|(-5(-1sin(2\u03c0x - 3)) + 4) - 2| - 2) - 2 and g(x) = (-1(1|(3x^2 + 5x + 3) + 2| - 2) - 2)/(-2(1|(3x^2 + 5x + 3) + 2| - 2) + 3) between the vertical lines x = 1.1 and x = 1.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-5(2sin(3\u03c0(3x + 5)) - 2)^2 - 1(2sin(3\u03c0(3x + 5)) - 2) - 1) - 3)/(2(-5(2sin(3\u03c0(3x + 5)) - 2)^2 - 1(2sin(3\u03c0(3x + 5)) - 2) - 1) + 3) and g(x) = -2|((-1(-3x^2 - 4x + 2) - 1)/(2(-3x^2 - 4x + 2) - 3)) + 3| between the vertical lines x = -1.3 and x = -0.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3sin(1\u03c0(2(-1x + 1)^2 + 5(-1x + 1) - 1) - 2) + 3) + 3)/(-1(-3sin(1\u03c0(2(-1x + 1)^2 + 5(-1x + 1) - 1) - 2) + 3) - 1) and g(x) = 3e^(1((-3(-3|x| + 3) + 2)/(-2(-3|x| + 3) - 2))) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-2|((-3x - 3)/(-3x + 2)) + 2| - 2)^2 + 5(-2|((-3x - 3)/(-3x + 2)) + 2| - 2) + 2 and g(x) = (-1(-3|x - 2|))/(3(-3|x - 2|) - 2) 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|((-2x - 3)/(-2x + 3)) + 2| - 1) - 4 and g(x) = -3(3sin(2\u03c0x + 2) + 1)^2 + 1(3sin(2\u03c0x + 2) + 1) 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-1(2sin(3\u03c0x + 3) - 1)^2 + 2(2sin(3\u03c0x + 3) - 1) + 4) + 1)/(3(-1(2sin(3\u03c0x + 3) - 1)^2 + 2(2sin(3\u03c0x + 3) - 1) + 4) - 2) and g(x) = (2(3|x - 1| + 2) + 1)/(-2(3|x - 1| + 2) - 3) 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-3|(-1x - 3) - 2| + 1) + 3)/(1(-3|(-1x - 3) - 2| + 1)), g(x) = -1|(-4x - 4) - 1| + 3, x = -4.5, 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-3|(-2sin(1\u03c0x - 1) - 1) + 1| - 3) - 3 and g(x) = -1|(-3x^2 + 2x + 2) + 1| between the vertical lines x = -1.6 and x = 2.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(1((2x + 2)/(-2x + 3)) - 5)^2 - 1(1((2x + 2)/(-2x + 3)) - 5) + 2 and g(x) = 3|(-3sin(2\u03c0x + 3) + 2) + 1| + 2 between the vertical lines x = 1.0 and x = 1.2. 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) = -2|((-3(2cos(2\u03c0x - 1) - 3))/(1(2cos(2\u03c0x - 1) - 3) + 2)) - 3| - 2, g(x) = -4(2cos(3\u03c0x - 3) - 2)^2 - 4(2cos(3\u03c0x - 3) - 2) - 5, 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": "34.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(2(3cos(3\u03c0x) + 2)) + 3)/(-3(2(3cos(3\u03c0x) + 2)) + 4) and g(x) = -1cos(2\u03c0(4x + 5) + 1) + 3 between the vertical lines x = -2.9 and x = -2.4. 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(-4(-2cos(1\u03c0(-2x - 4) - 1) + 1)^2 - 4) - 3)/(-3(-4(-2cos(1\u03c0(-2x - 4) - 1) + 1)^2 - 4) - 2), g(x) = (-3(-1|(-4x - 1) + 1| + 2) + 2)/(-3(-1|(-4x - 1) + 1| + 2) + 1), 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2e^(-1(-2|(-5((1x + 2)/(-1x - 3))^2) + 1| - 2)) - 1 and g(x) = 5(-2(3sin(1\u03c0x + 2) + 2) + 5)^2 - 2(-2(3sin(1\u03c0x + 2) + 2) + 5) + 4 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": "17.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3e^(1(1(3x^2 - 4x - 1) - 4)) + 1 and g(x) = 3sin(3\u03c0((2x - 2)/(-2x + 1)) + 2) - 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-1(-5(1|x + 2| + 1) - 5) + 2)/(3(-5(1|x + 2| + 1) - 5) + 3))^2 - 4((-1(-5(1|x + 2| + 1) - 5) + 2)/(3(-5(1|x + 2| + 1) - 5) + 3)) - 3 and g(x) = (-2(4(-3|x + 1| + 2) - 4) - 1)/(-1(4(-3|x + 1| + 2) - 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": "6.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2(1sin(2\u03c0x) - 1)^2 - 3(1sin(2\u03c0x) - 1) - 1) + 1)/(-2(2(1sin(2\u03c0x) - 1)^2 - 3(1sin(2\u03c0x) - 1) - 1) + 3) and g(x) = (-2(-1sin(3\u03c0x - 3)) - 3)/(-2(-1sin(3\u03c0x - 3)) + 3) from x = -2.0 to x = -1.9. 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": "Find the area of the region bounded by the curves f(x) = 1(3|((-2(-2sin(1\u03c0x + 3) + 1) - 1)/(2(-2sin(1\u03c0x + 3) + 1) - 3)) - 2| - 3) - 4, g(x) = 1((1(-2e^(1x) - 1))/(-1(-2e^(1x) - 1)))^2 - 3, x = -2.8, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-3cos(1\u03c0(2x^2 + 2x + 1)) + 1) + 1| + 1 and g(x) = 1(-2e^(1x) + 1) - 2 from x = -2.5 to x = -2.4. 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) = -5(3e^(-1(-2|x + 1| + 1))) + 5 and g(x) = -3sin(3\u03c0(-4x^2 + 3) - 2) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(3\u03c0(-3(-1|x - 2| + 1) + 1) + 2) + 3 and g(x) = 3(-5x^2 + 2x + 2) - 5 from x = 0.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-3((1x + 3)/(1x + 2))^2 + 4((1x + 3)/(1x + 2)) + 3) - 2| - 2, g(x) = -1sin(3\u03c0(3|x + 3| - 2)) - 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((-2(1e^(2(-2|x + 2| + 1)) + 2) + 1)/(-2(1e^(2(-2|x + 2| + 1)) + 2) - 1))^2 + 3((-2(1e^(2(-2|x + 2| + 1)) + 2) + 1)/(-2(1e^(2(-2|x + 2| + 1)) + 2) - 1)) + 3 and g(x) = -2(-3|(-2e^(1x) - 1) + 3| + 3) - 1 from x = -2.6 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(1|(1x^2 - 1x - 5) + 2| + 2) - 1)/(-3(1|(1x^2 - 1x - 5) + 2| + 2) + 4) and g(x) = 5(-3cos(1\u03c0x - 1) + 1)^2 + 4(-3cos(1\u03c0x - 1) + 1) - 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((3(1(-2|x + 2| - 1) - 3) + 1)/(-1(1(-2|x + 2| - 1) - 3) + 2))^2 + 1((3(1(-2|x + 2| - 1) - 3) + 1)/(-1(1(-2|x + 2| - 1) - 3) + 2)) + 2 and g(x) = 3|(-1(4x^2 - 3x - 2) + 2) + 1| + 1 from x = -0.7 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2|((3(3x) - 3)/(-2(3x) + 3)) + 1| + 3)^2 - 1(-2|((3(3x) - 3)/(-2(3x) + 3)) + 1| + 3) + 1 and g(x) = 1cos(1\u03c0(1|(-1x + 2) - 1|)) + 3 between the vertical lines x = 3.6 and x = 4.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = 4(3|((3(3x^2 + 3x - 5) - 3)/(-1(3x^2 + 3x - 5) - 3)) + 2| + 2) + 4 and g(x) = (-3(-1|(-2x - 3) - 1|))/(-2(-1|(-2x - 3) - 1|) - 1) between the vertical lines x = -2.3 and x = -1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-2((-2(-1|x|) - 3)/(-1(-1|x|) + 2)) - 1)^2 + 1(-2((-2(-1|x|) - 3)/(-1(-1|x|) + 2)) - 1) and g(x) = (-3(-2(-2|x + 1| + 2)^2 - 4(-2|x + 1| + 2) + 4) - 1)/(-1(-2(-2|x + 1| + 2)^2 - 4(-2|x + 1| + 2) + 4) - 3) between the vertical lines x = -1.6 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-1(-4((-2x)/(-3x - 3))^2 - 1((-2x)/(-3x - 3)) - 4) - 5) + 2| - 3 and g(x) = -3|(-5((3x + 1)/(1x + 2))^2 - 5((3x + 1)/(1x + 2)) + 2) + 3| + 1 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": "-24.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((3(-1e^(1(1x + 2)) + 3) - 1)/(-1(-1e^(1(1x + 2)) + 3))) - 2| - 3, g(x) = (-1(4(-1|x - 2| - 2) - 2) + 3)/(1(4(-1|x - 2| - 2) - 2) + 2), x = -1.0, 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": "22.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((3(3x^2 - 5x - 2) - 2)/(-3(3x^2 - 5x - 2) - 3)) - 1| + 3 and g(x) = (-1(-3|x + 3| + 2) - 2)/(2(-3|x + 3| + 2) - 1) between the vertical lines x = -3.6 and x = -2.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(3(2|(-2x + 5) - 3|)^2 + 4(2|(-2x + 5) - 3|) + 1) - 2)/(3(3(2|(-2x + 5) - 3|)^2 + 4(2|(-2x + 5) - 3|) + 1) + 2) and g(x) = -5(-1(-2|x - 3| + 2)^2 + 1) - 1 between the vertical lines x = 2.5 and x = 3.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(1\u03c0(-5((1(-3x^2 + 4x + 3) + 3)/(-2(-3x^2 + 4x + 3) - 3)) - 3) + 2) + 1, g(x) = (1(2sin(3\u03c0(-1|x - 2| - 2) + 3)) + 2)/(-1(2sin(3\u03c0(-1|x - 2| - 2) + 3)) - 3), x = 2.0, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-2((1x + 1)/(3x - 2))^2 - 1((1x + 1)/(3x - 2)) + 3) + 1 and g(x) = 3|(-4x + 3) - 2| - 2 from x = 0.4 to x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-21.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(5(3|x + 2|)^2 + 1(3|x + 2|)) + 5) - 1)/(3(-1(5(3|x + 2|)^2 + 1(3|x + 2|)) + 5) + 3) and g(x) = -4(2e^(2((-2x - 2)/(1x - 2))) - 1)^2 - 1(2e^(2((-2x - 2)/(1x - 2))) - 1) + 1 from x = -3.9 to x = -1.2. 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) = -3|(-1(5((2x + 1)/(3x + 2))^2 + 3)) - 3| - 3 and g(x) = (-3(1(-1sin(3\u03c0x + 3) + 2)^2 + 2(-1sin(3\u03c0x + 3) + 2) - 5) - 1)/(-2(1(-1sin(3\u03c0x + 3) + 2)^2 + 2(-1sin(3\u03c0x + 3) + 2) - 5) - 1) between the vertical lines x = 1.8 and x = 1.9. 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": "Calculate the area enclosed between the functions f(x) = (1(-3|(-3x^2 + 3x + 3) + 3| + 2) - 2)/(2(-3|(-3x^2 + 3x + 3) + 3| + 2) - 1) and g(x) = -1(-3sin(1\u03c0x - 3) + 3)^2 - 3(-3sin(1\u03c0x - 3) + 3) + 2 from x = -2.7 to x = -2.4. 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(2e^(1(-1x^2 - 4x)) - 3) - 2)/(2(2e^(1(-1x^2 - 4x)) - 3) + 2) and g(x) = (2(1x^2 - 5x + 4))/(2(1x^2 - 5x + 4)) from x = -4.0 to x = -0.0. 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": "Determine the area of the region enclosed by the graphs of f(x) = 3|((2(3(-4x - 2)^2 - 1(-4x - 2) - 1) - 2)/(-3(3(-4x - 2)^2 - 1(-4x - 2) - 1) - 3))| - 2 and g(x) = -3cos(1\u03c0((3(3x^2 + 5x - 5) + 1)/(-2(3x^2 + 5x - 5) + 1)) + 3) + 2 between the vertical lines x = -2.5 and 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": "Find the area of the region bounded by the curves f(x) = -1|(4(1((2x + 3)/(2x - 1))^2 - 4((2x + 3)/(2x - 1)) - 2) - 4) - 1| + 2, g(x) = -1((2(2sin(3\u03c0x - 1) + 1) - 1)/(-1(2sin(3\u03c0x - 1) + 1) + 3)) + 4, x = -1.0, 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": "2.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-2(-4(-4(1cos(3\u03c0x + 2))^2 + 5(1cos(3\u03c0x + 2)) - 1) - 4) + 3)/(3(-4(-4(1cos(3\u03c0x + 2))^2 + 5(1cos(3\u03c0x + 2)) - 1) - 4)) and g(x) = 3((-1(1x^2 + 2) + 1)/(-1(1x^2 + 2))) + 4 between the vertical lines x = -2.0 and x = -0.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(-2cos(3\u03c0(-2x^2 - 1x + 1) - 2) + 1) - 2)/(-1(-2cos(3\u03c0(-2x^2 - 1x + 1) - 2) + 1) + 2), g(x) = 3e^(-1(-4x - 2)) - 2, 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": "32.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-1|(-3x + 4) - 1|)^2 + 4(-1|(-3x + 4) - 1|)) - 3)/(1(1(-1|(-3x + 4) - 1|)^2 + 4(-1|(-3x + 4) - 1|))), g(x) = 5(-2|(3x - 4) + 1| + 3)^2 - 4(-2|(3x - 4) + 1| + 3) - 3, x = 0.4, 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": "0.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(2(-3x - 5)^2 - 1(-3x - 5) - 5))/(2(2(-3x - 5)^2 - 1(-3x - 5) - 5) - 1) and g(x) = -3((-1x - 1)/(-3x - 3)) from x = -2.2 to x = -1.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3|((1(-3sin(3\u03c0x) + 3) - 1)/(1(-3sin(3\u03c0x) + 3) + 3)) - 2| - 3, g(x) = 2(-2|x| + 2) - 2, x = -0.2, 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": "Determine the area of the region enclosed by the graphs of f(x) = 1((-2(4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) - 4) + 2)/(-3(4(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) - 4) + 4)) and g(x) = (2(-2(-1x^2 + 3x - 3) + 5) - 3)/(1(-2(-1x^2 + 3x - 3) + 5)) between the vertical lines x = -0.8 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": "Calculate the area enclosed between the functions f(x) = (1(-4(-1|(-2x^2 + 5x + 4) + 1| + 1) - 4) + 3)/(-3(-4(-1|(-2x^2 + 5x + 4) + 1| + 1) - 4)) and g(x) = -2cos(3\u03c0(-5(-3|x - 3| + 1)^2 + 5(-3|x - 3| + 1) - 1) - 2) + 1 from x = 2.2 to x = 2.3000000000000003. 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) = -3e^(-1(2(3x + 4)^2 + 4(3x + 4) + 1)) - 1 and g(x) = -2(2|x - 1| - 3) + 1 from x = -1.9 to x = -1.4. 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": "Calculate the area enclosed between the functions f(x) = 1|((1(-4(5x - 5)^2) - 2)/(2(-4(5x - 5)^2) + 1)) - 1| - 1 and g(x) = (3(-2sin(2\u03c0(-2|x + 2| + 2) + 1) + 1) - 3)/(-1(-2sin(2\u03c0(-2|x + 2| + 2) + 1) + 1) + 2) from x = -3.6 to x = -3.3. 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) = -4(1sin(2\u03c0(2((2x - 1)/(1x + 1)) - 4) + 1))^2 + 5(1sin(2\u03c0(2((2x - 1)/(1x + 1)) - 4) + 1)) + 2 and g(x) = (2(-1cos(2\u03c0(-3|x + 3|) + 3) + 2))/(-3(-1cos(2\u03c0(-3|x + 3|) + 3) + 2)) from x = -1.2 to x = -1.0999999999999999. 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(2|(3x^2 + 2x - 1) + 1| + 1) - 2)/(-2(2|(3x^2 + 2x - 1) + 1| + 1) + 1) and g(x) = -2cos(2\u03c0(1x - 3) - 1) + 2 between the vertical lines x = -0.7 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) = 1(1((-2x + 2)/(2x))^2 + 1((-2x + 2)/(2x))) + 3, g(x) = -2|(2x^2 - 5x - 1) - 2| + 3, x = 3.0, 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": "Determine the area of the region enclosed by the graphs of f(x) = -2cos(3\u03c0(-4(-4((3x + 3)/(-1x - 2))^2 - 5((3x + 3)/(-1x - 2)) + 3) + 2) - 3) - 1 and g(x) = 1(4(-2|x + 2| + 1)^2 + 5(-2|x + 2| + 1) - 5) - 1 between the vertical lines x = -1.9 and x = -1.8. 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": "Calculate the area enclosed between the functions f(x) = 1((-2(-3|x + 2| + 2) - 3)/(2(-3|x + 2| + 2) - 1))^2 - 5((-2(-3|x + 2| + 2) - 3)/(2(-3|x + 2| + 2) - 1)) + 3 and g(x) = -3((2x - 1)/(-1x)) + 3 from x = -2.6 to x = -1.4. 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) = -3|(-2(-3cos(3\u03c0x - 3) - 1) + 2) + 1| + 2 and g(x) = -5(3x + 1)^2 - 5(3x + 1) - 5 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|((-1(-2(-3x^2 + 3x + 1) - 2) + 2)/(-2(-2(-3x^2 + 3x + 1) - 2) - 2)) - 1| + 1, g(x) = -3cos(1\u03c0(-2|(4x^2 + 1) - 1| - 3) + 2) + 2, x = 4.8, and x = 4.8999999999999995. 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((-3(-3x) - 3)/(2(-3x) + 3))^2 + 2((-3(-3x) - 3)/(2(-3x) + 3)) - 2 and g(x) = (2(-3|x + 1| + 3) + 1)/(3(-3|x + 1| + 3) + 1) from x = -2.1 to x = 0.1. Round 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) = -1(1|(1e^(-1x) + 2) + 3| - 2)^2 + 2(1|(1e^(-1x) + 2) + 3| - 2) and g(x) = (3(2cos(1\u03c0x - 3) + 2) - 2)/(3(2cos(1\u03c0x - 3) + 2) - 1) from x = 2.2 to x = 3.8. 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) = -3|(5(-2((1x - 1)/(-2x - 2))^2 + 3((1x - 1)/(-2x - 2))) + 2) + 1| + 2 and g(x) = (-1(-3|(1x - 5) + 2| - 2) + 2)/(3(-3|(1x - 5) + 2| - 2) + 2) from x = -0.5 to x = 1.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(4(-3|x + 3| - 1)^2 + 5(-3|x + 3| - 1) - 5) - 4 and g(x) = (1(1cos(3\u03c0x + 3)))/(3(1cos(3\u03c0x + 3)) + 1) from x = -3.3 to x = -3.2. 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) = 1((-2(3x^2 + 1x - 1) - 1)/(-1(3x^2 + 1x - 1) - 1)) + 5 and g(x) = (-3(3x + 5) + 3)/(1(3x + 5) + 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": "61.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3|(4((1x + 1)/(3x + 3))^2 - 2((1x + 1)/(3x + 3)) - 1) - 3| + 1 and g(x) = 2|(-1x^2 - 1x + 5)| - 2 from x = -4.1 to x = 3.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1cos(3\u03c0(2|(-1(-1x - 2)^2 + 3(-1x - 2) + 2) + 3| + 1) + 3) + 2 and g(x) = (-3(1(2|x + 1| + 1) + 4) + 3)/(-1(1(2|x + 1| + 1) + 4) - 2) from x = 3.5 to 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": "Calculate the area enclosed between the functions f(x) = (-1(2(-1sin(3\u03c0(1|x - 2|) + 1) + 1)) - 2)/(3(2(-1sin(3\u03c0(1|x - 2|) + 1) + 1)) + 3) and g(x) = -2e^(-2((-1(1|x - 1| - 2))/(2(1|x - 1| - 2) - 1))) + 1 from x = -1.1 to x = 3.1. 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": "Calculate the area enclosed between the functions f(x) = -4(-4(1|x| - 2) - 3)^2 + 4(-4(1|x| - 2) - 3) + 5 and g(x) = -2cos(2\u03c0(-1x - 3) - 3) from x = -0.9 to x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-2sin(1\u03c0(1(2x^2 + 4x + 2) - 2) + 3) - 1) + 2)/(1(-2sin(1\u03c0(1(2x^2 + 4x + 2) - 2) + 3) - 1) + 1) and g(x) = 3cos(2\u03c0(-1(3|x - 1| - 2) + 4)) + 1 from x = -3.8 to x = -3.6. 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": "Find the area of the region bounded by the curves f(x) = (-1(3(-2|(-2x + 1) - 1| - 1)^2 + 5(-2|(-2x + 1) - 1| - 1) - 2) - 3)/(-2(3(-2|(-2x + 1) - 1| - 1)^2 + 5(-2|(-2x + 1) - 1| - 1) - 2) - 3), g(x) = -2cos(2\u03c0(2|((1x + 1)/(3x)) - 1| - 1) + 3) - 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(-5(-1|((2x - 2)/(-2x + 1)) - 1| + 3)^2 + 2(-1|((2x - 2)/(-2x + 1)) - 1| + 3) + 4) - 2 and g(x) = -1|((2(4x - 1) + 2)/(-1(4x - 1) + 2)) - 3| + 1 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": "59.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-3|((1(3x^2 + 3x - 3) - 1)/(2(3x^2 + 3x - 3) + 1))| - 2) - 2 and g(x) = -4((-2(1|x + 2| + 3) - 1)/(1(1|x + 2| + 3) + 1)) - 1 between the vertical lines x = -1.7 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1sin(1\u03c0(5(2|x - 3| - 3) + 3) + 3) - 2 and g(x) = (-2(5x + 4) + 1)/(3(5x + 4) + 2) 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) = 1(1cos(3\u03c0((-2x + 1)/(1x - 3)) + 2) + 3)^2 - 2(1cos(3\u03c0((-2x + 1)/(1x - 3)) + 2) + 3) + 4 and g(x) = -3sin(2\u03c0((2x + 1)/(-2x + 1)) + 1) + 2 between the vertical lines x = 3.1 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) = -5(2|((-2(5x^2 + 2x - 1) - 3)/(-3(5x^2 + 2x - 1) + 1)) - 1| - 2) - 3, g(x) = 1((1(-1|x - 2| + 3) - 2)/(-1(-1|x - 2| + 3) + 3)), 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": "62.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-1(3|(3x^2 - 4x - 2)|) + 3)/(3(3|(3x^2 - 4x - 2)|) + 2)) - 5 and g(x) = (3(2(-3cos(2\u03c0x - 1) - 1)^2 + 5(-3cos(2\u03c0x - 1) - 1) + 3) - 2)/(2(2(-3cos(2\u03c0x - 1) - 1)^2 + 5(-3cos(2\u03c0x - 1) - 1) + 3) - 1) from x = -3.0 to x = -2.1. 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) = 3cos(2\u03c0((1(4(1|x + 1| - 2) + 3) - 1)/(2(4(1|x + 1| - 2) + 3) + 3))) - 3 and g(x) = -4(1|((-1x + 3)/(-3x + 1)) - 1| - 2)^2 - 4(1|((-1x + 3)/(-3x + 1)) - 1| - 2) - 5 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1sin(1\u03c0(2|(2x^2 - 2x - 2) + 3| + 3) + 1) - 2))/(1(-1sin(1\u03c0(2|(2x^2 - 2x - 2) + 3| + 3) + 1) - 2) + 2), g(x) = -2|(-3(5x^2 + 2x - 2) + 4) - 3| + 2, 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": "3.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3((-3(-3|x - 1| + 1) - 3)/(-3(-3|x - 1| + 1) - 1)) - 3 and g(x) = 1cos(3\u03c0(5x^2 + 2x + 5) + 1) - 2 between the vertical lines x = 1.6 and x = 1.7000000000000002. 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(-2sin(2\u03c0(-3|(2x^2 + 1x + 2) - 2| - 3)) - 3) - 4 and g(x) = 5(-3(-2sin(1\u03c0x + 1) + 1) - 4)^2 + 3(-3(-2sin(1\u03c0x + 1) + 1) - 4) from x = 4.1 to x = 4.199999999999999. 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) = 3cos(3\u03c0((2(-2(-1|x - 3| - 2) + 1) - 2)/(1(-2(-1|x - 3| - 2) + 1) + 1)) - 2) + 2 and g(x) = 5((-2(-1|x - 2| + 1) + 1)/(-2(-1|x - 2| + 1) - 3))^2 + 2((-2(-1|x - 2| + 1) + 1)/(-2(-1|x - 2| + 1) - 3)) + 3 between the vertical lines x = 0.7 and x = 2.6. 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) = -4((1(3|x - 3| - 1) - 2)/(2(3|x - 3| - 1) + 3)) + 4 and g(x) = 2|(-1x^2 - 5x - 5) + 3| - 3 between the vertical lines x = -1.3 and x = 0.2. 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": "Find the area of the region bounded by the curves f(x) = 3|(2((3(-1x - 3) + 3)/(3(-1x - 3) + 3))^2 + 3((3(-1x - 3) + 3)/(3(-1x - 3) + 3)) - 3)| - 3, g(x) = (3(2e^(2(2x^2 - 1x - 3)) - 1) + 1)/(-1(2e^(2(2x^2 - 1x - 3)) - 1) + 2), x = -1.0, 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": "8.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(2cos(2\u03c0(2(3|x + 3| + 1)^2 + 2(3|x + 3| + 1) - 4) + 2)) - 3)/(3(2cos(2\u03c0(2(3|x + 3| + 1)^2 + 2(3|x + 3| + 1) - 4) + 2)) - 2) and g(x) = 1(-4((-1x - 3)/(-2x + 3)) + 2)^2 + 3(-4((-1x - 3)/(-2x + 3)) + 2) - 5 from x = 3.7 to x = 3.8000000000000003. 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(-1(5(-2|x + 3|)^2 + 4(-2|x + 3|) + 4) + 3))/(1(-1(5(-2|x + 3|)^2 + 4(-2|x + 3|) + 4) + 3) + 2) and g(x) = 3|(5(-1x + 5)^2 - 4) - 1| - 2 between the vertical lines x = 4.0 and x = 4.1. 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(1e^(2(-3(-3|x - 2| - 1)^2 - 2(-3|x - 2| - 1) - 4)) + 2) - 2)/(-1(1e^(2(-3(-3|x - 2| - 1)^2 - 2(-3|x - 2| - 1) - 4)) + 2) - 1), g(x) = -1|(-5(5x + 2)^2 + 4(5x + 2))| + 1, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5((-3(5x^2 + 3x + 1) + 3)/(3(5x^2 + 3x + 1) - 1)) + 5 and g(x) = 1(-1|x - 1| - 3)^2 + 1(-1|x - 1| - 3) - 4 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-1(3|(3x - 3) + 1| + 1)^2 + 5(3|(3x - 3) + 1| + 1) - 5) - 2)/(3(-1(3|(3x - 3) + 1| + 1)^2 + 5(3|(3x - 3) + 1| + 1) - 5) - 2) and g(x) = (-2(-2|(3x + 5) + 2| - 1) - 1)/(3(-2|(3x + 5) + 2| - 1) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-2((-1x - 2)/(2x)) - 2) + 1| - 1, g(x) = -2|((2x + 2)/(1x - 3))| - 3, x = -1.0, 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": "93.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((-3(3x^2 + 4x - 5) + 2)/(1(3x^2 + 4x - 5))) + 3 and g(x) = (-2(1|x - 3| + 3) - 3)/(3(1|x - 3| + 3) - 2) between the vertical lines x = -2.2 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1cos(2\u03c0((3(-2x) + 1)/(-1(-2x) + 2)) + 2) - 3 and g(x) = 1(2sin(1\u03c0x - 1))^2 - 1(2sin(1\u03c0x - 1)) - 3 between the vertical lines x = 0.6 and x = 2.2. Round 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) = (1(1e^(1(-1(-1x + 4)^2 - 1(-1x + 4) + 2)) - 1))/(-1(1e^(1(-1(-1x + 4)^2 - 1(-1x + 4) + 2)) - 1) + 3) and g(x) = 5(3|(-3sin(2\u03c0x - 3) - 1) - 1| - 3) - 2 between the vertical lines x = -4.6 and x = -4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1|(-2(2x + 3)^2 + 4(2x + 3) + 1) - 1| + 3, g(x) = -2sin(3\u03c0(2x^2 - 1x - 2) + 3) - 3, x = -2.0, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(3sin(2\u03c0(-4(1|x + 3| - 1)^2 - 4(1|x + 3| - 1) + 5) + 2)) - 4 and g(x) = (2(-3sin(1\u03c0(2x^2 - 4x + 2) + 3) - 3) + 2)/(-2(-3sin(1\u03c0(2x^2 - 4x + 2) + 3) - 3) + 3) between the vertical lines x = 1.7 and x = 1.8. 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": "Find the area of the region bounded by the curves f(x) = -4(-3(-1sin(2\u03c0x - 3) + 1)^2 - 2(-1sin(2\u03c0x - 3) + 1)) - 1, g(x) = 1|(4x^2 + 4x + 3) - 3| - 1, 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": "12.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(-1(3cos(2\u03c0(-2|x + 1| + 2) + 2) - 1) - 4)^2 - 3(-1(3cos(2\u03c0(-2|x + 1| + 2) + 2) - 1) - 4) + 1 and g(x) = (-2(-2|(3e^(-1x) + 1) - 2| + 1))/(-2(-2|(3e^(-1x) + 1) - 2| + 1) - 3) from x = 0.0 to x = 0.6. 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(1(2|x - 3|) - 4) - 2)/(2(1(2|x - 3|) - 4) + 2) and g(x) = 3(2cos(3\u03c0x) - 1)^2 + 2(2cos(3\u03c0x) - 1) + 4 between the vertical lines x = 1.6 and x = 4.4. Round 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) = -2|(5(-4(1sin(3\u03c0x - 2) - 3)^2 - 4(1sin(3\u03c0x - 2) - 3) + 3) + 2) + 1| - 1, g(x) = -1(3|(2sin(2\u03c0x - 2) - 2) + 1| - 2)^2 - 3(3|(2sin(2\u03c0x - 2) - 2) + 1| - 2) - 5, 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(1|(-2x - 3) - 3| + 2) + 3)/(-2(1|(-2x - 3) - 3| + 2) - 2), g(x) = 3(3sin(2\u03c0x + 2) - 1)^2 + 2(3sin(2\u03c0x + 2) - 1) - 3, x = 3.6, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((1(-1|(-2x^2 + 5x - 3) - 3|) - 1)/(-3(-1|(-2x^2 + 5x - 3) - 3|) - 1)) - 3, g(x) = -5(4(-1e^(1x) + 3) + 3)^2 - 4(4(-1e^(1x) + 3) + 3) + 3, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0((-3(1|x - 3| + 3) - 2)/(-1(1|x - 3| + 3) + 2)) + 3) + 3 and g(x) = -3(2sin(3\u03c0x + 1) + 1) + 3 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": "2.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5(-3((-2x - 3)/(-2x - 1)) + 2)^2 + 2(-3((-2x - 3)/(-2x - 1)) + 2) + 4 and g(x) = 1|(-1x + 5) - 3| - 1 from x = -3.2 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": "Calculate the area enclosed between the functions f(x) = 2e^(-1(1(-2|x + 3|)^2 + 2(-2|x + 3|))) - 2 and g(x) = 2cos(3\u03c0((-1x - 1)/(2x + 3)) + 3) - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2sin(1\u03c0(-3((1(-4x + 2) - 3)/(-3(-4x + 2) - 1))^2 - 1)) - 2 and g(x) = -2|(1((-2x + 2)/(-3x + 1))) - 3| - 1 from x = 0.0 to x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1e^(1(-3|(1((2x - 2)/(2x - 3)) - 2) - 3| + 1)) - 1, g(x) = (1(-3(4x - 1)^2 + 1(4x - 1) - 3) - 2)/(-2(-3(4x - 1)^2 + 1(4x - 1) - 3) - 1), x = 0.2, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3sin(3\u03c0((-2(-2x + 3) - 1)/(-1(-2x + 3) + 2)) + 3) - 2 and g(x) = 2(-2cos(1\u03c0x - 1) + 1)^2 + 5(-2cos(1\u03c0x - 1) + 1) - 3 from x = -3.3 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(1\u03c0(-3(3(1|x - 2| + 2) - 5)^2 + 3(3(1|x - 2| + 2) - 5) + 2) + 1), g(x) = (2(3(-2cos(2\u03c0x + 3) - 1)^2 - 3(-2cos(2\u03c0x + 3) - 1) - 4))/(-1(3(-2cos(2\u03c0x + 3) - 1)^2 - 3(-2cos(2\u03c0x + 3) - 1) - 4) - 1), 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1e^(1((-2(-1|x - 1| + 3) + 2)/(-2(-1|x - 1| + 3) - 2))) + 2 and g(x) = -3|((3x + 3)/(-1x - 2)) - 2| + 2 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": "Calculate the area enclosed between the functions f(x) = (-1(-4(1|(-3x^2 + 2x + 3) + 2| - 2) + 1) - 3)/(-2(-4(1|(-3x^2 + 2x + 3) + 2| - 2) + 1) + 3) and g(x) = -4(-2cos(1\u03c0((1x)/(-3x - 2)) + 2) - 2)^2 - 1(-2cos(1\u03c0((1x)/(-3x - 2)) + 2) - 2) - 2 from x = -0.7 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(1(3|(-2x^2 - 5x - 5) + 1| - 3) - 2))/(-1(1(3|(-2x^2 - 5x - 5) + 1| - 3) - 2) - 3) and g(x) = -5((1(1|x + 3| - 2) + 2)/(-3(1|x + 3| - 2) - 2)) + 5 from x = -4.1 to x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-2(-2|(2cos(1\u03c0x) + 1) - 3| - 1) - 5) - 1)/(-1(-2(-2|(2cos(1\u03c0x) + 1) - 3| - 1) - 5) - 2) and g(x) = -2|((3(-5x + 4))/(-3(-5x + 4))) - 1| + 3 from x = 2.2 to x = 3.8. 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) = 2|(-3e^(-1((2(-2x + 3) - 1)/(3(-2x + 3) + 2))) - 3) + 3| - 2 and g(x) = 2((-1(1|x - 1| - 2) + 3)/(-3(1|x - 1| - 2))) + 3 from x = -1.9 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(4(-3e^(2(-1|x - 3| + 1)) + 2) + 1) + 1)/(-2(4(-3e^(2(-1|x - 3| + 1)) + 2) + 1) - 2) and g(x) = 2sin(2\u03c0(-1(3|x + 2| - 3) + 3)) - 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(1\u03c0(-2|((2x + 1)/(-2x + 1))| + 3) + 3) - 3, g(x) = -3(-5x - 4)^2 - 2(-5x - 4) - 4, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1(2(2|x + 1| + 3)^2 + 5(2|x + 1| + 3) - 5) - 2) - 1)/(1(-1(2(2|x + 1| + 3)^2 + 5(2|x + 1| + 3) - 5) - 2) + 3), g(x) = 4(2(-2|x - 1| + 3)^2 - 5(-2|x - 1| + 3) - 2) + 3, 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|((-2(3(-4x + 1)^2 + 1(-4x + 1) - 1))/(-1(3(-4x + 1)^2 + 1(-4x + 1) - 1) + 2)) - 1| - 2 and g(x) = -4(2|((3x + 3)/(-2x - 3)) - 1| - 1)^2 - 2(2|((3x + 3)/(-2x - 3)) - 1| - 1) + 2 from x = -1.3 to x = -1.0. 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(-2|(-2cos(1\u03c0x - 1) + 1)| + 2) - 2)/(-1(-2|(-2cos(1\u03c0x - 1) + 1)| + 2) - 3), g(x) = (1(2x^2 + 1x + 2) + 1)/(-1(2x^2 + 1x + 2) - 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": "6.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-2|(2cos(3\u03c0(-1x^2 + 1x - 3) + 1) + 1) - 2| - 2) - 4, g(x) = -1cos(3\u03c0(-4((2x)/(2x - 1))^2 + 2((2x)/(2x - 1)) + 2) - 1), x = 2.8, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-1(-2cos(2\u03c0x - 3) - 1) - 1) + 2)/(-3(-1(-2cos(2\u03c0x - 3) - 1) - 1) - 3) and g(x) = -1sin(2\u03c0(-1x + 5)) from x = 1.6 to x = 2.2. 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": "Find the area of the region bounded by the curves f(x) = -1((3(3|(2x - 1)| - 2) - 2)/(1(3|(2x - 1)| - 2) + 1))^2 + 1((3(3|(2x - 1)| - 2) - 2)/(1(3|(2x - 1)| - 2) + 1)) - 2, g(x) = -1|(-1(2sin(1\u03c0x))^2 + 5(2sin(1\u03c0x)) + 5) + 1| + 2, x = -0.6, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(1(-2|(2x^2 - 5x - 3) - 3| + 1) + 4) + 3)/(-3(1(-2|(2x^2 - 5x - 3) - 3| + 1) + 4) + 2), g(x) = (1(1|(-1x + 5) - 2| + 3) - 1)/(1(1|(-1x + 5) - 2| + 3)), x = -0.5, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-2(-1x - 4) + 3)/(2(-1x - 4) - 1)) - 2| and g(x) = (-2(-1|x + 1| + 3) + 3)/(-2(-1|x + 1| + 3) + 1) between the vertical lines x = -3.4 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2e^(2(-2(-1x^2 - 3x - 2) - 5)) + 2, g(x) = 1|(2sin(3\u03c0x + 3) - 1)| + 3, x = -3.2, 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": "7.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-5(2|(-2x - 2) + 2| + 2)^2 + 2(2|(-2x - 2) + 2| + 2) - 5) - 1)/(2(-5(2|(-2x - 2) + 2| + 2)^2 + 2(2|(-2x - 2) + 2| + 2) - 5) - 3) and g(x) = (1(1(-3x + 4)^2 + 4(-3x + 4) + 4) + 3)/(3(1(-3x + 4)^2 + 4(-3x + 4) + 4) + 1) 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1e^(1(4((-2(-3x - 5) + 1)/(3(-3x - 5)))^2 + 2((-2(-3x - 5) + 1)/(3(-3x - 5))) + 1)) + 1, g(x) = 1(3|(1x + 2) + 3|)^2 - 5(3|(1x + 2) + 3|) + 3, x = -4.4, 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((2(-1(-3|x + 1| - 3) + 4) + 3)/(-2(-1(-3|x + 1| - 3) + 4) + 3))^2 + 1((2(-1(-3|x + 1| - 3) + 4) + 3)/(-2(-1(-3|x + 1| - 3) + 4) + 3)) + 5 and g(x) = (-3(-2e^(1(-1|x| + 2)) + 3) - 1)/(-1(-2e^(1(-1|x| + 2)) + 3)) 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": "13.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(3(-2x^2 - 1x + 1) + 3) - 2)/(-3(3(-2x^2 - 1x + 1) + 3) + 1) and g(x) = 4(-1sin(1\u03c0x) - 3)^2 - 2(-1sin(1\u03c0x) - 3) - 4 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": "82.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(-1|(-1((1x)/(2x + 1)) - 3)|)^2 + 1(-1|(-1((1x)/(2x + 1)) - 3)|) + 4 and g(x) = 5(3|(-5x^2 - 1x + 3) - 1| + 2) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 3sin(2\u03c0(3|(-1x - 3)| - 1)) + 2, g(x) = -2(-1e^(1x) - 3) - 5, 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": "Determine the area of the region enclosed by the graphs of f(x) = -1|((3(1(2x - 5)^2 + 2(2x - 5) - 5) - 3)/(3(1(2x - 5)^2 + 2(2x - 5) - 5) + 2)) + 1| and g(x) = -1(-3|(1cos(1\u03c0x - 2) - 3) + 2| - 2)^2 + 3(-3|(1cos(1\u03c0x - 2) - 3) + 2| - 2) - 2 between the vertical lines x = 0.9 and x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(5(-3|x| - 1)^2 - 3(-3|x| - 1) + 5) - 3)/(3(5(-3|x| - 1)^2 - 3(-3|x| - 1) + 5) + 1), g(x) = -2(-2|x - 2| + 3), 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(2(1cos(2\u03c0(4x + 1) + 2))^2 + 5(1cos(2\u03c0(4x + 1) + 2)) - 5) + 3| + 3 and g(x) = -5((3(2|x - 1| - 2))/(3(2|x - 1| - 2) - 2))^2 + 1((3(2|x - 1| - 2))/(3(2|x - 1| - 2) - 2)) + 2 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((1(5x - 4) - 3)/(-2(5x - 4) + 1)) + 3| + 3 and g(x) = 3(-1cos(3\u03c0x - 1) - 3)^2 + 3(-1cos(3\u03c0x - 1) - 3) + 1 from x = -4.3 to x = -4.2. 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(-3e^(-2(2(-3|x| - 3)^2 - 1(-3|x| - 3) - 3)) - 2) - 2)/(2(-3e^(-2(2(-3|x| - 3)^2 - 1(-3|x| - 3) - 3)) - 2) + 1), g(x) = -1(3|(2e^(-1x)) - 3| - 1) - 1, x = -0.5, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|((1(-2x + 1) - 3)/(2(-2x + 1) + 1)) - 1| + 1 and g(x) = (1(1|x - 3| + 2) + 3)/(-2(1|x - 3| + 2) - 2) from x = -2.0 to x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((-1(4(2x^2 - 1x) + 2) + 1)/(-2(4(2x^2 - 1x) + 2) + 3)) + 3| - 2 and g(x) = (2(-4(1|x + 2| - 2)) - 2)/(-1(-4(1|x + 2| - 2)) + 3) between the vertical lines x = -3.1 and x = -0.9. 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) = -3(1|(3x - 1) - 3| - 2)^2 - 2(1|(3x - 1) - 3| - 2) + 1, g(x) = 3(-3|x + 1| - 1) + 1, x = 0.1, 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": "58.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2|((-2(-5x^2 + 5x + 2))/(-3(-5x^2 + 5x + 2) - 2)) - 2| - 2) - 3 and g(x) = 1|(-1((2x - 2)/(-1x)) + 4) + 3| + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-4(2|x + 1| - 1)^2 - 2(2|x + 1| - 1) + 1) + 5 and g(x) = -1(2|x + 2| + 2)^2 + 1(2|x + 2| + 2) + 5 between the vertical lines x = -1.8 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(-5(2|((2x)/(3x - 2)) - 3| - 3) + 4)^2 - 4(-5(2|((2x)/(3x - 2)) - 3| - 3) + 4) - 4 and g(x) = -4(-4(2cos(3\u03c0x + 1) - 2) - 1)^2 + 1(-4(2cos(3\u03c0x + 1) - 2) - 1) - 4 between the vertical lines x = -2.2 and x = -2.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|(4(-3cos(2\u03c0((-3x)/(-1x + 2)) - 3) - 2) - 2) + 3| - 3, g(x) = 4(-3(3|x - 2| - 3)^2 + 5) - 5, x = 1.7, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2((1(1|(-5x - 3) + 2| + 1) + 1)/(1(1|(-5x - 3) + 2| + 1) + 3))^2 - 2((1(1|(-5x - 3) + 2| + 1) + 1)/(1(1|(-5x - 3) + 2| + 1) + 3)), g(x) = -2(4(-3cos(2\u03c0x + 1) + 2) - 2)^2 + 4(4(-3cos(2\u03c0x + 1) + 2) - 2) - 1, x = 1.6, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-2|(5(1x^2 + 4x + 1) - 3) + 2|) + 2)/(1(-2|(5(1x^2 + 4x + 1) - 3) + 2|) + 3) and g(x) = -1e^(1((-2(-3x^2 + 3x - 5))/(-3(-3x^2 + 3x - 5) - 1))) - 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": "17.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(3sin(3\u03c0(-3(3x + 5)^2 + 1(3x + 5) - 5) + 3) - 1) - 1| + 3 and g(x) = -3sin(1\u03c0((3(-1x^2 + 4x + 4) + 1)/(-1(-1x^2 + 4x + 4) - 2)) - 3) + 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|((-1(3x - 1) + 2)/(2(3x - 1) - 3)) + 1| - 2, g(x) = 1(-2|x + 3| - 1)^2 + 2(-2|x + 3| - 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": "11.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-3cos(1\u03c0(3|x - 2| + 2) + 3) - 1) - 1)/(2(-3cos(1\u03c0(3|x - 2| + 2) + 3) - 1)) and g(x) = 1((1x - 1)/(3x + 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(1e^(2(-3|((-2x + 2)/(-3x + 4)) + 1| - 2)) + 3)^2 + 5 and g(x) = 1((-3(-3x^2 + 2x + 4) - 1)/(-2(-3x^2 + 2x + 4) + 1)) + 5 between the vertical lines x = -0.8 and x = 1.5. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-4(2x - 1)^2 + 2(2x - 1) + 3) - 1)/(3(-4(2x - 1)^2 + 2(2x - 1) + 3) - 2) and g(x) = -1e^(2((1x - 2)/(-2x - 2))) - 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(5((3x - 2)/(2x + 2)) - 4)^2 - 2(5((3x - 2)/(2x + 2)) - 4) + 1 and g(x) = 3sin(1\u03c0(4x^2 + 4x - 2)) + 1 between the vertical lines x = 3.2 and x = 3.3000000000000003. 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((-2(2|(-5x - 3) - 2| - 2))/(1(2|(-5x - 3) - 2| - 2) + 3))^2 + 3((-2(2|(-5x - 3) - 2| - 2))/(1(2|(-5x - 3) - 2| - 2) + 3)) + 5 and g(x) = 1((-3(1|x - 2| + 1) - 2)/(2(1|x - 2| + 1) - 1))^2 + 3((-3(1|x - 2| + 1) - 2)/(2(1|x - 2| + 1) - 1)) - 1 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2|(-1((-2x - 2)/(3x - 1)) + 3)| + 1)^2 - 4(-2|(-1((-2x - 2)/(3x - 1)) + 3)| + 1) + 4, g(x) = (2(4(-4x - 5)^2 + 1(-4x - 5) - 4) + 2)/(2(4(-4x - 5)^2 + 1(-4x - 5) - 4) - 1), x = -1.5, 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": "87.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(5((3x)/(-2x + 3)) - 4)^2 - 4(5((3x)/(-2x + 3)) - 4) - 2, g(x) = 3(-2sin(3\u03c0x - 3) - 1) + 5, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(3(-5x^2 + 5x - 4) + 5) + 3)/(-2(3(-5x^2 + 5x - 4) + 5) + 1), g(x) = 2(-3|x|)^2 - 2(-3|x|) - 2, x = -0.3, 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((-3(-1(-2e^(1x) - 2) + 5) - 2)/(2(-1(-2e^(1x) - 2) + 5) - 1))^2 - 2((-3(-1(-2e^(1x) - 2) + 5) - 2)/(2(-1(-2e^(1x) - 2) + 5) - 1)) - 5 and g(x) = 4(-1|(-1x) - 3| + 2)^2 + 2(-1|(-1x) - 3| + 2) - 1 from x = -2.3 to x = 0.7. 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|(-3x^2 - 4x + 1) + 3| + 1) and g(x) = -1((-1x - 1)/(-1x + 3)) + 5 between the vertical lines x = -1.5 and x = 0.1. 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) = -3sin(3\u03c0(5(-2x + 5)^2 - 3(-2x + 5) + 2)) - 2, g(x) = -1sin(2\u03c0(2|x| + 3)) + 2, x = -4.6, 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": "8.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2sin(2\u03c0((3(-1|(3x^2 + 3x) + 3| + 2) - 2)/(-1(-1|(3x^2 + 3x) + 3| + 2) - 2)) - 3) + 2, g(x) = -2e^(-1((3(-5x^2 - 2x + 3) + 3)/(-2(-5x^2 - 2x + 3) - 3))) + 1, x = -1.1, 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": "14.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3|(5(2x - 3)^2 - 1(2x - 3) - 1) - 2| + 2) + 3)/(3(-3|(5(2x - 3)^2 - 1(2x - 3) - 1) - 2| + 2) - 2) and g(x) = 1(3cos(3\u03c0(-4x^2 + 2x + 3) + 3)) from x = 4.7 to x = 4.8. 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) = -1sin(2\u03c0(3|((2x + 2)/(1x + 3)) + 2| + 2) - 3) - 3, g(x) = 3sin(1\u03c0(-2|x + 2| + 2) - 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(3sin(1\u03c0((2x + 3)/(-2x - 3)) - 2) - 3)^2 + 2(3sin(1\u03c0((2x + 3)/(-2x - 3)) - 2) - 3) + 5 and g(x) = 2|(3cos(2\u03c0x - 1) + 2)| + 2 between the vertical lines x = -4.6 and 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) = (1(1|(-2x - 1) + 1| - 1) - 1)/(3(1|(-2x - 1) + 1| - 1) - 2) and g(x) = 1|((-2x + 1)/(-1x + 3)) - 2| + 1 between the vertical lines x = -0.8 and 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": "Calculate the area enclosed between the functions f(x) = 3((-3(-2|(3x - 2) - 2| + 3) + 3)/(-3(-2|(3x - 2) - 2| + 3) + 2))^2 - 4((-3(-2|(3x - 2) - 2| + 3) + 3)/(-3(-2|(3x - 2) - 2| + 3) + 2)) - 5 and g(x) = (-1(1(-3cos(1\u03c0x)) + 3) - 3)/(-2(1(-3cos(1\u03c0x)) + 3) - 2) from x = 1.0 to x = 1.7. 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) = 3(-2(2cos(3\u03c0((1x - 2)/(-2x - 1)) - 3) + 3) + 1)^2 - 4(-2(2cos(3\u03c0((1x - 2)/(-2x - 1)) - 3) + 3) + 1) and g(x) = 1|((3(1x) - 1)/(-3(1x) + 4))| - 1 between the vertical lines x = 1.3 and x = 1.4000000000000001. 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": "Calculate the area enclosed between the functions f(x) = 1|(1((1x - 3)/(3x)) - 1) - 1| and g(x) = -1((-2x)/(-1x - 2)) + 4 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": "45.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3e^(2(2((2(2|x - 3| + 1))/(2(2|x - 3| + 1) + 3))^2 - 5((2(2|x - 3| + 1))/(2(2|x - 3| + 1) + 3)) + 2)) and g(x) = -1|(2(-1x^2 - 5x - 5) + 1) - 2| + 3 from x = -4.1 to x = -0.9. 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(3sin(3\u03c0(-5((-3x)/(-3x + 1)) + 2) - 2) - 3)^2 - 5(3sin(3\u03c0(-5((-3x)/(-3x + 1)) + 2) - 2) - 3) - 2 and g(x) = 2cos(2\u03c0(1|(-5x + 5) + 2| + 2)) - 3 between the vertical lines x = 1.8 and x = 2.5. 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) = -3cos(2\u03c0(3(-4((-2x + 1)/(1x)) - 2)^2 - 2(-4((-2x + 1)/(1x)) - 2) + 3) + 3) + 2 and g(x) = 2|(3e^(1((1x - 1)/(-2x + 1))) - 3) - 1| + 1 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3(-3(-3|(2sin(2\u03c0x) - 2)| + 3)^2 + 1(-3|(2sin(2\u03c0x) - 2)| + 3) + 3) - 1 and g(x) = -3(-2|(2cos(3\u03c0x - 1) + 1) + 2| - 1)^2 - 3(-2|(2cos(3\u03c0x - 1) + 1) + 2| - 1) + 3 between the vertical lines x = 1.2 and x = 1.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3(3cos(2\u03c0(2|x - 3|) + 2))^2 - 4(3cos(2\u03c0(2|x - 3|) + 2)) + 2) - 2)/(2(-3(3cos(2\u03c0(2|x - 3|) + 2))^2 - 4(3cos(2\u03c0(2|x - 3|) + 2)) + 2) + 3) and g(x) = (-1(-1(-1|x + 2| + 3) - 2) - 1)/(-3(-1(-1|x + 2| + 3) - 2) + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-3sin(3\u03c0(1|(3x - 3) - 1| + 3) + 1) - 3)^2 - 2(-3sin(3\u03c0(1|(3x - 3) - 1| + 3) + 1) - 3) and g(x) = -1|(3(-1e^(-1x) + 2)^2 - 4(-1e^(-1x) + 2) + 4) - 2| + 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": "3.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(3|(-1x) + 2|)^2 - 2(3|(-1x) + 2|) + 4 and g(x) = -2((-1x + 1)/(-1x))^2 - 3((-1x + 1)/(-1x)) - 4 between the vertical lines x = 0.1 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2(-3sin(1\u03c0x - 3) - 1)^2 + 3(-3sin(1\u03c0x - 3) - 1) + 4) - 2, g(x) = -3e^(1(1x^2 - 3x - 5)) + 1, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-2(-3|(5(1cos(2\u03c0x)) + 3) - 2| + 2) - 2)/(1(-3|(5(1cos(2\u03c0x)) + 3) - 2| + 2) + 3) and g(x) = -2|(3(1cos(1\u03c0x - 2))^2 - 1(1cos(1\u03c0x - 2)) + 2) - 3| - 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3|(-1(1e^(-2((-1x + 2)/(-3x - 2))) + 3) - 2) + 1| + 1 and g(x) = -5(3sin(1\u03c0(-2|x - 2| + 2) + 2) + 3) - 5 between the vertical lines x = -4.4 and x = -3.7. 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) = 1sin(2\u03c0(1((3(4x^2 - 3x + 4) - 3)/(-1(4x^2 - 3x + 4) + 2))) - 3), g(x) = 2((-1(2|x + 2|) + 2)/(-3(2|x + 2|)))^2 - 5((-1(2|x + 2|) + 2)/(-3(2|x + 2|))) + 1, x = 1.0, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4((-1(-5x - 2) + 2)/(2(-5x - 2) - 1))^2 - 5((-1(-5x - 2) + 2)/(2(-5x - 2) - 1)) and g(x) = -1e^(2(3x - 1)) - 1 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(2sin(1\u03c0(2x + 4) - 1) + 3) + 3| - 1 and g(x) = 4(1e^(-1x) + 1) - 5 between the vertical lines x = -1.2 and 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": "Find the area of the region bounded by the curves f(x) = -1|((-1(3x^2 - 1x - 1))/(-2(3x^2 - 1x - 1) + 3)) + 1| + 1, g(x) = (-2(1cos(2\u03c0x - 3) + 3))/(1(1cos(2\u03c0x - 3) + 3) + 3), x = -0.7, 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(2(2e^(-1x) - 2)^2 + 4(2e^(-1x) - 2) - 4)| + 2 and g(x) = 2cos(3\u03c0((1x - 2)/(-2x - 3)) - 1) - 2 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": "Calculate the area enclosed between the functions f(x) = -5(-1|(3sin(2\u03c0x + 1) - 2) - 3| + 3)^2 - 3(-1|(3sin(2\u03c0x + 1) - 2) - 3| + 3) - 3 and g(x) = (-2(-2cos(2\u03c0x - 2) + 1) + 1)/(-2(-2cos(2\u03c0x - 2) + 1)) from x = 2.5 to x = 3.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((-3(3(3cos(3\u03c0x + 1) - 3)^2 - 4) - 1)/(-3(3(3cos(3\u03c0x + 1) - 3)^2 - 4))) - 2 and g(x) = -1|(2(-4x - 2)^2 + 5(-4x - 2) - 2) + 3| 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) = 1|(5(-4x + 4)^2 - 3(-4x + 4) - 1)| + 1 and g(x) = 4(3x^2 + 1) + 4 between the vertical lines x = 0.5 and x = 1.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1sin(2\u03c0(1|x + 2| + 2) + 3) - 3) - 2)/(-3(1sin(2\u03c0(1|x + 2| + 2) + 3) - 3) - 2) and g(x) = 3cos(1\u03c0(-2x - 4) - 1) - 1 between the vertical lines x = 3.0 and x = 3.7. 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": "Determine the area of the region enclosed by the graphs of f(x) = -2|(2cos(2\u03c0(-5(-1x + 3)^2 + 4(-1x + 3) + 1)) + 1) + 3| + 2 and g(x) = -5(2e^(1(1|x + 3| - 2)) - 2) - 1 between the vertical lines x = -0.8 and x = -0.7000000000000001. 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) = (3(-2cos(1\u03c0(2x + 5) + 2) + 2) - 3)/(-3(-2cos(1\u03c0(2x + 5) + 2) + 2)) and g(x) = 5(3|x| - 3)^2 + 5(3|x| - 3) + 2 between the vertical lines x = 2.2 and x = 2.3000000000000003. 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) = 1((-3(-1|(1x - 4) - 2| + 2) + 3)/(-2(-1|(1x - 4) - 2| + 2)))^2 + 4((-3(-1|(1x - 4) - 2| + 2) + 3)/(-2(-1|(1x - 4) - 2| + 2))) - 4, g(x) = -2(-3cos(3\u03c0(3|x + 2| + 3) + 3) + 1)^2 + 1(-3cos(3\u03c0(3|x + 2| + 3) + 3) + 1) + 5, x = 4.6, 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": "1.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-5(2x^2 + 1x - 1)) + 3)/(2(-5(2x^2 + 1x - 1)) - 1), g(x) = (1(-5x^2 + 4x - 5) - 1)/(-3(-5x^2 + 4x - 5) - 3), x = -0.8, 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": "Determine the area of the region enclosed by the graphs of f(x) = -3|((-2(1(1x^2 - 3x + 5) + 2) + 3)/(3(1(1x^2 - 3x + 5) + 2) + 1)) + 3| + 2 and g(x) = -5(-3|((-2x - 2)/(-1x - 3)) + 2| - 1)^2 - 5(-3|((-2x - 2)/(-1x - 3)) + 2| - 1) - 2 between the vertical lines x = -2.0 and x = -1.9. 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|((-2(-5(-2x^2 - 5x - 2) - 2) + 2)/(-2(-5(-2x^2 - 5x - 2) - 2) - 3)) + 3| + 2, g(x) = (-1(-2(4x^2 - 5x + 3)) - 1)/(2(-2(4x^2 - 5x + 3)) + 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": "5.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-5(3(-2|x + 3|)^2 + 1(-2|x + 3|) - 3) - 3) - 1)/(1(-5(3(-2|x + 3|)^2 + 1(-2|x + 3|) - 3) - 3) - 2) and g(x) = 2(-3sin(1\u03c0(2|x| + 3) - 1) + 3)^2 + 5(-3sin(1\u03c0(2|x| + 3) - 1) + 3) - 2 from x = 3.0 to x = 3.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1|((1(2e^(2x) + 2) + 3)/(-1(2e^(2x) + 2) - 3)) - 2| and g(x) = 5(4x^2 + 3x - 1) + 5 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": "4.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((1(4x - 3) - 1)/(2(4x - 3) + 2)) + 2| + 3 and g(x) = (2(-3sin(1\u03c0x) - 2) + 1)/(-2(-3sin(1\u03c0x) - 2) + 1) 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": "13.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-3|(-5x - 3) + 3| - 2) - 1)/(1(-3|(-5x - 3) + 3| - 2)) and g(x) = (-2(5x + 2) - 1)/(2(5x + 2) + 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-1((-1(-3|x + 1| + 2) + 2)/(1(-3|x + 1| + 2)))^2 - 4((-1(-3|x + 1| + 2) + 2)/(1(-3|x + 1| + 2))) + 1) - 3 and g(x) = 2((-3(1x) + 1)/(-2(1x) + 3))^2 - 1((-3(1x) + 1)/(-2(1x) + 3)) - 5 between the vertical lines x = 1.1 and x = 2.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-42.8", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 5(4(-3|((1x + 2)/(-3x + 1)) + 3| + 2)^2 - 1) - 1 and g(x) = 5(4(-2|x - 1| + 3)^2 - 2(-2|x - 1| + 3)) + 2 from x = 0.5 to x = 1.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2(-3(-1sin(1\u03c0((1x - 1)/(1x + 2))) - 2) - 5)^2 - 2(-3(-1sin(1\u03c0((1x - 1)/(1x + 2))) - 2) - 5) + 4 and g(x) = 1|(3((-2x - 1)/(2x))^2 - 3) - 3| - 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": "12.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (2(-3(1(1cos(2\u03c0x)) + 3)^2 - 5(1(1cos(2\u03c0x)) + 3) + 4) + 3)/(-1(-3(1(1cos(2\u03c0x)) + 3)^2 - 5(1(1cos(2\u03c0x)) + 3) + 4) + 2), g(x) = (-2(-4(3x - 2)^2 + 5(3x - 2) + 5) - 1)/(2(-4(3x - 2)^2 + 5(3x - 2) + 5) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(2((-1(5x + 2) - 2)/(-1(5x + 2) - 3))^2 - 1((-1(5x + 2) - 2)/(-1(5x + 2) - 3)) - 3) - 1| + 3 and g(x) = -2cos(2\u03c0(3(-5x^2 - 2x + 1) - 3) - 2) + 3 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": "-3.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(-1(-5((-2x - 2)/(-2x - 1)) - 2)^2 - 5(-5((-2x - 2)/(-2x - 1)) - 2) - 4)| - 1 and g(x) = -1e^(1(-2(-1x + 2)^2 - 3(-1x + 2))) - 2 from x = -1.4 to x = -1.3. 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) = 3|((-3(5x) + 1)/(-1(5x) + 2)) - 2| - 2 and g(x) = 2sin(1\u03c0(-3x - 2) - 3) - 1 from x = -3.7 to x = -3.2. 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) = (-2(-3(2(3|x - 2| - 1)^2 + 4(3|x - 2| - 1) + 5) + 5) + 3)/(-1(-3(2(3|x - 2| - 1)^2 + 4(3|x - 2| - 1) + 5) + 5) + 2), g(x) = 2|((3(-3x^2 - 5x - 3) + 1)/(-3(-3x^2 - 5x - 3) + 1))|, x = 1.6, 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(-5(2cos(1\u03c0x - 1) - 2) - 5) + 1)/(3(-5(2cos(1\u03c0x - 1) - 2) - 5) + 1), g(x) = 2|((-1x + 2)/(-3x)) + 1| + 1, x = 2.6, 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": "6.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2|(-4(1((-3x - 1)/(-2x + 3)) + 5)^2 - 2(1((-3x - 1)/(-2x + 3)) + 5) - 5) - 2| - 3 and g(x) = 3|(1(-2cos(2\u03c0x + 3))^2 + 5(-2cos(2\u03c0x + 3))) - 3| + 3 between the vertical lines x = 1.0 and x = 1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(2|((-1x + 2)/(1x)) - 2| + 1) - 3, g(x) = 4(-1sin(2\u03c0x) + 1)^2 + 1(-1sin(2\u03c0x) + 1) + 4, 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": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(-1e^(1(3|x - 2| - 1)) + 3) - 4, g(x) = -5(-1sin(3\u03c0x + 1)) - 5, x = 1.3, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-1(2sin(3\u03c0(2x^2 - 2x) - 3) + 2) - 4) + 3)/(-2(-1(2sin(3\u03c0(2x^2 - 2x) - 3) + 2) - 4) - 1) and g(x) = (1(4(1x^2 + 3x - 3) + 5))/(1(4(1x^2 + 3x - 3) + 5) - 2) from x = -0.9 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": "Determine the area of the region enclosed by the graphs of f(x) = (2(2(-1(2|x + 2| + 3)^2 + 3(2|x + 2| + 3) + 3) + 4) + 1)/(1(2(-1(2|x + 2| + 3)^2 + 3(2|x + 2| + 3) + 3) + 4) + 1) and g(x) = -2((1(-1cos(2\u03c0x + 3) + 3) + 3)/(2(-1cos(2\u03c0x + 3) + 3) + 1))^2 + 3((1(-1cos(2\u03c0x + 3) + 3) + 3)/(2(-1cos(2\u03c0x + 3) + 3) + 1)) - 4 between the vertical lines x = -2.6 and x = -1.4. 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) = (3(-3(-1|(3x - 5) - 3| + 1)^2 - 2(-1|(3x - 5) - 3| + 1) + 4) - 3)/(-3(-3(-1|(3x - 5) - 3| + 1)^2 - 2(-1|(3x - 5) - 3| + 1) + 4) - 2), g(x) = (-2(-5(-3sin(2\u03c0x + 1))^2 - 5(-3sin(2\u03c0x + 1)) - 4) - 1)/(-2(-5(-3sin(2\u03c0x + 1))^2 - 5(-3sin(2\u03c0x + 1)) - 4) - 1), x = 2.7, 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2cos(2\u03c0(-2((-1x + 1)/(2x + 1))) + 1) + 3, g(x) = (-1(-1x^2 - 4x - 2) - 2)/(-3(-1x^2 - 4x - 2) + 1), x = -3.2, 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": "5.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2|(-1(1x + 4)^2 - 5(1x + 4) - 2) - 2| + 1) + 1)/(-1(-2|(-1(1x + 4)^2 - 5(1x + 4) - 2) - 2| + 1) + 2) and g(x) = -1(-5(2|x + 2| - 3) + 5)^2 - 5(-5(2|x + 2| - 3) + 5) between the vertical lines x = -4.5 and x = -4.0. 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) = (-2(3|(1(-4x)^2 - 5(-4x) - 2) - 2| - 2) - 2)/(-1(3|(1(-4x)^2 - 5(-4x) - 2) - 2| - 2)), g(x) = (-1(3|(3e^(1x) - 1) - 3| + 2) - 1)/(1(3|(3e^(1x) - 1) - 3| + 2)), x = -1.4, 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": "5.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(-3sin(2\u03c0(-1(2x + 4)^2 + 2(2x + 4) - 3) - 1) - 3) + 1)/(-3(-3sin(2\u03c0(-1(2x + 4)^2 + 2(2x + 4) - 3) - 1) - 3) - 1) and g(x) = (-2(-1|(1x^2 + 1x + 1) - 1| + 1))/(-2(-1|(1x^2 + 1x + 1) - 1| + 1) + 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(3\u03c0(-1(5((-1x - 3)/(3x)) + 4)^2 - 1(5((-1x - 3)/(3x)) + 4) + 1) + 2), g(x) = 2|(2sin(1\u03c0(3x + 2) - 1) + 2) - 3| + 2, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2e^(-2(1(1|x + 2| + 3)^2 - 4(1|x + 2| + 3) + 2)) + 2 and g(x) = -4(-1cos(3\u03c0x - 2) - 1) - 1 between the vertical lines x = -1.3 and x = -0.9. 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) = (2(-1(-2cos(3\u03c0(-2|x - 3|) - 2) + 3) - 2))/(2(-1(-2cos(3\u03c0(-2|x - 3|) - 2) + 3) - 2) - 1) and g(x) = -1|(4((1x + 2)/(-2x + 1)) - 4) - 2| + 3 between the vertical lines x = -0.3 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": "Calculate the area enclosed between the functions f(x) = 3((-2(2x^2 - 1x + 4) - 3)/(-3(2x^2 - 1x + 4) + 4)) and g(x) = -3(2cos(3\u03c0x + 2) - 2) - 4 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": "2.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((3(1(-2e^(-2x))^2 + 2(-2e^(-2x)) - 3) + 1)/(-3(1(-2e^(-2x))^2 + 2(-2e^(-2x)) - 3) + 4)) + 3, g(x) = 2(3cos(2\u03c0(1|x - 2| - 3) - 3) - 1)^2 - 5(3cos(2\u03c0(1|x - 2| - 3) - 3) - 1), x = -4.7, and x = -4.3. 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) = -1|(-1(1((-3x + 1)/(2x + 1))^2 - 5((-3x + 1)/(2x + 1)) - 4) + 3) - 2| + 2, g(x) = (3(-1(3|x| + 2) - 2) + 2)/(2(-1(3|x| + 2) - 2)), x = 1.2, 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3sin(2\u03c0(3(1x + 1)^2 + 4(1x + 1) + 2) - 3) + 2, g(x) = (2(2x^2 + 4x + 1) + 2)/(-2(2x^2 + 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": "Determine the area of the region enclosed by the graphs of f(x) = 4((-1(2|(1x^2 + 2x + 1) - 3| + 1) + 3)/(1(2|(1x^2 + 2x + 1) - 3| + 1) - 2)) - 5 and g(x) = 5(-5((2x - 1)/(1x))^2 + 2((2x - 1)/(1x)) - 1) - 2 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": "51.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(3(-1|(1e^(2x)) - 2| + 1) - 1) + 1)/(-2(3(-1|(1e^(2x)) - 2| + 1) - 1) - 3) and g(x) = (-2(3|(-4x + 2) + 1| + 1))/(-1(3|(-4x + 2) + 1| + 1) - 1) from x = 0.0 to 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(-1(-2|x| + 1) + 4)) + 1 and g(x) = 3cos(1\u03c0(1x - 3) - 3) + 1 between the vertical lines x = -3.5 and x = -2.6. 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) = (-1(-2|(2(-3x^2 - 2x + 1) + 2)| + 3) - 3)/(2(-2|(2(-3x^2 - 2x + 1) + 2)| + 3) - 3) and g(x) = (-2(3(3cos(1\u03c0x) - 2) + 2) - 2)/(-3(3(3cos(1\u03c0x) - 2) + 2) + 1) between the vertical lines x = -4.4 and x = -3.6. 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": "Determine the area of the region enclosed by the graphs of f(x) = 4((-2(-1|(4x - 3)| - 1) + 3)/(3(-1|(4x - 3)| - 1) + 2))^2 + 3((-2(-1|(4x - 3)| - 1) + 3)/(3(-1|(4x - 3)| - 1) + 2)) - 5 and g(x) = -5((-3(-2|x + 1| + 1) - 3)/(-2(-2|x + 1| + 1) + 3))^2 - 4((-3(-2|x + 1| + 1) - 3)/(-2(-2|x + 1| + 1) + 3)) between the vertical lines x = -1.4 and x = -0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1cos(3\u03c0(-3(-1|x| - 2)^2 - 5(-1|x| - 2) - 3) - 3) + 1 and g(x) = 1(-2|x - 1| + 3) between the vertical lines x = 1.7 and x = 1.8. 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) = -2(-2((2(-2|x + 1| - 1))/(1(-2|x + 1| - 1) - 3))^2 + 5((2(-2|x + 1| - 1))/(1(-2|x + 1| - 1) - 3)) + 2) + 4 and g(x) = (-2(-3|(-5x - 1) + 1|) + 2)/(3(-3|(-5x - 1) + 1|) + 2) between the vertical lines x = -0.1 and x = 0.1. 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) = (-1(3sin(2\u03c0(-2(3|x + 1| + 1)^2 - 5(3|x + 1| + 1)) - 2) + 1) - 3)/(-2(3sin(2\u03c0(-2(3|x + 1| + 1)^2 - 5(3|x + 1| + 1)) - 2) + 1) - 2) and g(x) = 3((-1(-1|x - 3|) + 3)/(3(-1|x - 3|) - 2)) - 3 between the vertical lines x = 2.1 and 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": "Determine the area of the region enclosed by the graphs of f(x) = -4(-2sin(2\u03c0(-5(-1|x + 1| + 2)^2 - 3) + 2) + 2) + 3 and g(x) = 2sin(2\u03c0(-3(5x - 3)^2 - 1(5x - 3) + 3) + 3) between the vertical lines x = 2.7 and x = 2.8000000000000003. 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) = (-2(-5(3|(-4x + 2) + 2| - 1)^2 - 2(3|(-4x + 2) + 2| - 1) + 1) + 2)/(2(-5(3|(-4x + 2) + 2| - 1)^2 - 2(3|(-4x + 2) + 2| - 1) + 1)) and g(x) = 1|((-1(3e^(-2x) + 3) + 2)/(1(3e^(-2x) + 3) + 2)) - 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3|(-1(-3((2x + 2)/(-1x - 2))^2 + 2((2x + 2)/(-1x - 2)) + 3) + 4) - 1| and g(x) = 3((3(2x^2 + 4) + 2)/(2(2x^2 + 4))) between the vertical lines x = -1.4 and x = -0.7. 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": "Calculate the area enclosed between the functions f(x) = 2|((3(3(1x^2 + 5x + 1) + 2) + 2)/(-1(3(1x^2 + 5x + 1) + 2) - 2)) + 2| - 1 and g(x) = 1(3|((-2x - 3)/(-1x + 3)) - 3| - 1)^2 + 4(3|((-2x - 3)/(-1x + 3)) - 3| - 1) + 4 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": "13.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-2(-2(-1|x + 3| - 1))^2 - 2) - 1)/(-3(-2(-2(-1|x + 3| - 1))^2 - 2) - 2) and g(x) = 2|(1(4x^2 - 1x + 3) - 5)| - 2 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-1|(3e^(-1(2x^2 + 2x + 4)))| + 2) - 3)/(3(-1|(3e^(-1(2x^2 + 2x + 4)))| + 2) - 2), g(x) = (3(-2(2|x| + 1)^2 + 4(2|x| + 1)) - 2)/(2(-2(2|x| + 1)^2 + 4(2|x| + 1)) - 3), x = -0.3, 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": "27.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(-4(1|((2x + 3)/(2x)) - 1| + 1)^2 - 2(1|((2x + 3)/(2x)) - 1| + 1)) + 1, g(x) = 3(-1((-3x)/(2x - 1))^2 + 2((-3x)/(2x - 1)) - 4) - 1, x = 0.4, 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": "-42.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((1(4(3|x + 1| - 3) - 3) + 1)/(3(4(3|x + 1| - 3) - 3)))^2 + 2((1(4(3|x + 1| - 3) - 3) + 1)/(3(4(3|x + 1| - 3) - 3))) + 1 and g(x) = 2(-3cos(2\u03c0(-3x^2 - 5x + 5) + 1) - 2) + 2 from x = 4.4 to x = 4.5. 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|((2(-1sin(2\u03c0x - 1) - 3) + 3)/(1(-1sin(2\u03c0x - 1) - 3) + 1)) - 1|, g(x) = -2(2|x + 1| - 1) + 2, x = -2.0, 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": "5.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2((2(-2sin(3\u03c0x - 1) + 1) - 2)/(-1(-2sin(3\u03c0x - 1) + 1) - 1)) - 3 and g(x) = (3(-3|x + 3| - 3))/(-1(-3|x + 3| - 3) - 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": "Determine the area of the region enclosed by the graphs of f(x) = -2((2(2|(-3x^2 + 5x + 3) + 1|) - 2)/(1(2|(-3x^2 + 5x + 3) + 1|) + 2)) + 5 and g(x) = -2sin(2\u03c0(-2|((-1x + 3)/(-2x - 1)) + 2| + 3) + 2) + 2 between the vertical lines x = -1.2 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) = -4((-3(-3|(1x + 4)| + 3) + 1)/(-1(-3|(1x + 4)| + 3) + 2))^2 - 1((-3(-3|(1x + 4)| + 3) + 1)/(-1(-3|(1x + 4)| + 3) + 2)) + 3, g(x) = -1|(1cos(3\u03c0(3x + 4) - 1) + 1) + 1| + 2, x = -3.2, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3|((-1(1x^2 - 2x) + 1)/(2(1x^2 - 2x) + 2)) - 2| + 1, g(x) = 3e^(2((2x + 1)/(-1x - 1))) - 2, x = 0.5, 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": "-22.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1|(-4(-2cos(2\u03c0(-2x^2 - 2x) - 3) + 3) + 4) - 2| - 3 and g(x) = -2|(-1((-3x + 1)/(2x + 3)) + 2)| + 2 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(-5(2sin(1\u03c0x + 3) + 2)^2 + 2) + 1 and g(x) = (-3(-2sin(2\u03c0x - 2) - 3) + 3)/(-2(-2sin(2\u03c0x - 2) - 3) + 3) from x = 4.3 to x = 4.8. 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|((1(1x + 5) + 2)/(2(1x + 5) + 2)) - 2| - 3 and g(x) = (3(1|x + 2| - 1) - 1)/(-3(1|x + 2| - 1) + 2) between the vertical lines x = -4.1 and x = 0.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-2e^(2((2(-2x + 3) + 3)/(1(-2x + 3)))) - 1) - 2| - 1, g(x) = -1((3(2cos(3\u03c0x - 3) + 1))/(-3(2cos(3\u03c0x - 3) + 1) + 4)) - 1, x = 3.1, 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": "20.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 5(-3(-3sin(2\u03c0(3|x| + 1) - 1) + 3)^2 + 5(-3sin(2\u03c0(3|x| + 1) - 1) + 3) + 1) + 3, g(x) = 1((-1(2cos(3\u03c0x - 3) + 1) + 1)/(3(2cos(3\u03c0x - 3) + 1) - 2))^2 - 5((-1(2cos(3\u03c0x - 3) + 1) + 1)/(3(2cos(3\u03c0x - 3) + 1) - 2)) + 5, x = 4.5, 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": "44.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(2(-2|(-1x^2 + 1x + 2) - 2| - 2) - 5) - 1)/(-2(2(-2|(-1x^2 + 1x + 2) - 2| - 2) - 5) - 2), g(x) = -4(2sin(3\u03c0(-2|x - 3| - 1) + 3))^2 + 4(2sin(3\u03c0(-2|x - 3| - 1) + 3)) + 3, x = -2.0, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1|(-2cos(1\u03c0(-3x + 4) + 1) - 3) - 2| - 3 and g(x) = -1((1x + 3)/(3x))^2 - 1((1x + 3)/(3x)) + 5 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": "-14.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(-3cos(3\u03c0((1(1|x + 1| - 2) + 3)/(2(1|x + 1| - 2) + 3)) + 2) + 1)^2 + 1(-3cos(3\u03c0((1(1|x + 1| - 2) + 3)/(2(1|x + 1| - 2) + 3)) + 2) + 1) + 5 and g(x) = 1(3|(2cos(2\u03c0x + 3) + 3) - 1| + 3)^2 + 2(3|(2cos(2\u03c0x + 3) + 3) - 1| + 3) - 3 from x = -0.9 to x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(4((1x + 1)/(3x - 1))^2 - 3((1x + 1)/(3x - 1))) + 3 and g(x) = 3|(3x^2 + 2x - 2) + 1| + 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3e^(-1(-3|(-1x^2 + 2x + 4) + 2| - 1)) - 2 and g(x) = 3|(-2x - 5) - 1| - 2 between the vertical lines x = 3.5 and x = 3.7. 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) = -1e^(2(-4(1x + 1)^2 - 3(1x + 1) + 4)) + 3, g(x) = -2(-3e^(1x) + 3) - 2, 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|(1(-4((3x + 2)/(3x - 2))^2 + 2((3x + 2)/(3x - 2)) - 1) + 2) - 3| - 3 and g(x) = -1(-3(2cos(3\u03c0x + 3) - 3) - 4)^2 + 2(-3(2cos(3\u03c0x + 3) - 3) - 4) + 2 from x = -3.8 to x = -3.7. 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) = 2sin(1\u03c0((-2(-2|x| + 2) + 3)/(2(-2|x| + 2)))) + 2 and g(x) = 3(1|x - 2| + 1) between the vertical lines x = 1.9 and x = 2.3. 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) = -1(1|(-1x - 2) + 2| + 2)^2 + 1(1|(-1x - 2) + 2| + 2), g(x) = -2(-3x + 2)^2 + 3(-3x + 2) - 2, x = 0.1, 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (3(-5(1|(5x^2 + 5) - 3| - 2) + 2))/(-1(-5(1|(5x^2 + 5) - 3| - 2) + 2) + 3) and g(x) = 1(2|((-1x + 3)/(1x - 2)) + 1| - 2) - 2 from x = 0.8 to x = 4.0. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "85.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(5(1(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) - 5) - 3) - 1)/(2(5(1(-1|x + 3| - 3)^2 + 3(-1|x + 3| - 3) - 5) - 3) - 3), g(x) = -4(3cos(1\u03c0(-2|x - 2| - 2) + 1) + 2)^2 + 4, x = 2.9, 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": "30.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(1(-5(1|x - 1| - 2)^2 - 1(1|x - 1| - 2) + 1) + 1) - 3)/(1(1(-5(1|x - 1| - 2)^2 - 1(1|x - 1| - 2) + 1) + 1) - 3) and g(x) = -2|(2e^(-1((2x - 2)/(1x))) + 3) - 3| + 1 between the vertical lines x = -1.5 and x = -0.3. 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": "Determine the area of the region enclosed by the graphs of f(x) = (-1(-2(1(-1e^(-1x)) - 1)^2 - 2(1(-1e^(-1x)) - 1) + 3) - 3)/(-3(-2(1(-1e^(-1x)) - 1)^2 - 2(1(-1e^(-1x)) - 1) + 3) - 2) and g(x) = -3|(1(2x - 1)^2 + 3(2x - 1) + 1) - 2| + 1 between the vertical lines x = -1.1 and x = 0.0. 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) = 3|((-2(-2(1e^(-2x) + 2) + 3))/(-2(-2(1e^(-2x) + 2) + 3) + 3)) - 3| - 1, g(x) = -1((1(3|x| - 2))/(-2(3|x| - 2) - 2)) + 2, x = -0.3, 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": "1.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -5((-1(-2|x - 2|) - 1)/(-1(-2|x - 2|) - 2)) - 3 and g(x) = -2sin(1\u03c0(2|x| + 3) - 2) + 1 from x = 1.3 to x = 2.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-4(-2((3x - 3)/(-3x - 1)) - 1)^2 - 1(-2((3x - 3)/(-3x - 1)) - 1) - 5) - 3| + 3 and g(x) = 1|(-1((-3x - 1)/(3x - 2)) - 1) + 1| - 1 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": "42.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|((-1(3x^2 - 4x) + 2)/(-1(3x^2 - 4x) - 1)) + 3| - 2 and g(x) = -2|(-1sin(3\u03c0x - 2) + 2) - 3| + 2 from x = 1.2 to x = 1.4. 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": "Determine the area of the region enclosed by the graphs of f(x) = (1(2(3e^(-1(4x + 3)) - 2)^2 - 5(3e^(-1(4x + 3)) - 2) - 2) + 3)/(-1(2(3e^(-1(4x + 3)) - 2)^2 - 5(3e^(-1(4x + 3)) - 2) - 2) + 2) and g(x) = 2sin(1\u03c0(4(1|x + 1| + 3)^2 + 1(1|x + 1| + 3) + 4) - 2) - 1 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(1((1(5x - 5) + 2)/(-2(5x - 5) - 1))^2 + 4((1(5x - 5) + 2)/(-2(5x - 5) - 1)) + 1) - 2| + 2 and g(x) = 1sin(1\u03c0((2(-2|x - 2| + 1) + 3)/(3(-2|x - 2| + 1) - 1)) + 1) - 3 from x = 0.5 to 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": "Find the area of the region bounded by the curves f(x) = -3(-3((2x - 3)/(-3x)) + 1)^2 + 3(-3((2x - 3)/(-3x)) + 1) + 5, g(x) = (-2(-2sin(3\u03c0x - 3) + 2) + 1)/(2(-2sin(3\u03c0x - 3) + 2) + 3), x = 0.8, 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": "6.9", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-1(-2|(3(-3x^2 + 2x + 2) - 5) - 2| + 2) - 2)/(2(-2|(3(-3x^2 + 2x + 2) - 5) - 2| + 2) + 1), g(x) = (3(1(-2x + 3)^2 + 2(-2x + 3) - 2) - 1)/(3(1(-2x + 3)^2 + 2(-2x + 3) - 2)), x = 1.1, 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(3\u03c0(-3((-2x - 3)/(-1x - 3)) - 1)) and g(x) = 4(3sin(2\u03c0x) + 2) + 5 between the vertical lines x = -1.2 and x = 0.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(4(2|((-2x - 1)/(2x + 3)) - 2| - 1) - 5)^2 - 2(4(2|((-2x - 1)/(2x + 3)) - 2| - 1) - 5) + 4 and g(x) = -4(-2|(1sin(1\u03c0x - 2) + 2)| + 1)^2 - 5(-2|(1sin(1\u03c0x - 2) + 2)| + 1) - 3 between the vertical lines x = -1.2 and x = -1.1. 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": "Determine the area of the region enclosed by the graphs of f(x) = -1((-1(-3x^2 + 2x + 3) - 1)/(-1(-3x^2 + 2x + 3) + 2)) - 4 and g(x) = -4(5x^2 - 1x) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2|(-3((2(2x + 1) + 3)/(-1(2x + 1)))^2 + 5((2(2x + 1) + 3)/(-1(2x + 1))) + 5) + 2| - 2 and g(x) = 4((3(-3e^(2x) + 1) - 3)/(3(-3e^(2x) + 1) + 2))^2 - 4((3(-3e^(2x) + 1) - 3)/(3(-3e^(2x) + 1) + 2)) - 2 from x = -0.8 to x = -0.7000000000000001. 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": "Calculate the area enclosed between the functions f(x) = (2(-2(3|(1x^2 - 1x - 2)| + 3) - 1) - 1)/(-3(-2(3|(1x^2 - 1x - 2)| + 3) - 1) - 2) and g(x) = (-1(-3(-3|x - 1| - 2) - 3) - 3)/(2(-3(-3|x - 1| - 2) - 3) + 2) 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(3e^(2(1|x| - 1))) + 1)/(-2(3e^(2(1|x| - 1)))) and g(x) = (3(4x^2 - 4x - 5) + 2)/(3(4x^2 - 4x - 5) - 2) from x = -0.7 to x = 1.7. 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) = -3|((3(1x^2 - 4) + 3)/(-3(1x^2 - 4) + 4)) + 3| + 1 and g(x) = -3((-1x + 2)/(-1x - 1)) + 4 from x = -3.1 to x = -2.4. 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) = 5(1((3x + 1)/(2x - 1))^2 - 5((3x + 1)/(2x - 1)) + 4) - 4 and g(x) = 5(4x + 3)^2 + 1(4x + 3) + 4 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": "-124.7", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (2(-4(-3|x + 2| + 1) + 3) + 1)/(2(-4(-3|x + 2| + 1) + 3) - 1) and g(x) = (-2(5x^2 + 1x + 3) - 1)/(1(5x^2 + 1x + 3) + 3) 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2|((-1(5x - 4) + 3)/(-2(5x - 4) + 1)) - 2|)^2 + 3(2|((-1(5x - 4) + 3)/(-2(5x - 4) + 1)) - 2|) + 3 and g(x) = 5(-3cos(1\u03c0((1x - 1)/(-2x - 2)) - 2) - 2)^2 + 2(-3cos(1\u03c0((1x - 1)/(-2x - 2)) - 2) - 2) + 2 from x = -1.2 to x = -1.0999999999999999. 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) = 4(4(-3cos(2\u03c0((-2x - 3)/(-2x + 1)) - 2) + 3) - 4)^2 + 5(4(-3cos(2\u03c0((-2x - 3)/(-2x + 1)) - 2) + 3) - 4) - 5 and g(x) = 2((1(-1sin(2\u03c0x + 3) - 2) - 3)/(-3(-1sin(2\u03c0x + 3) - 2) - 2))^2 + 5((1(-1sin(2\u03c0x + 3) - 2) - 3)/(-3(-1sin(2\u03c0x + 3) - 2) - 2)) - 3 between the vertical lines x = 1.3 and x = 1.4000000000000001. 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) = (2(2|(1(5x^2 - 5x - 4) - 5) + 1| - 1) + 2)/(3(2|(1(5x^2 - 5x - 4) - 5) + 1| - 1) - 2) and g(x) = (2(2e^(1(2x))) + 2)/(3(2e^(1(2x))) - 1) 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2|(-3e^(-1(-4((1x + 2)/(2x - 1))^2 + 2((1x + 2)/(2x - 1)) - 5)) - 1) + 1| + 3 and g(x) = 4(-5((-2x + 2)/(-3x - 3))^2 - 1((-2x + 2)/(-3x - 3)) - 4) + 4 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": "-1200.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1((-1(1|(-1x + 2) - 3|))/(3(1|(-1x + 2) - 3|) - 2))^2 - 2((-1(1|(-1x + 2) - 3|))/(3(1|(-1x + 2) - 3|) - 2)) - 4 and g(x) = -4(-3|(1x + 5)| + 2)^2 + 3(-3|(1x + 5)| + 2) + 1 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-5x^2 + 1x - 5) + 1)/(-2(-5x^2 + 1x - 5) - 2)) - 1| + 3 and g(x) = 1|(2sin(3\u03c0x - 3) - 2) - 2| - 1 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (2(4(2sin(2\u03c0x + 1))^2 - 4(2sin(2\u03c0x + 1)) + 5) - 1)/(-1(4(2sin(2\u03c0x + 1))^2 - 4(2sin(2\u03c0x + 1)) + 5) - 3) and g(x) = 3cos(3\u03c0(1|x - 2| - 2) - 1) - 3 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|((-2(-2sin(3\u03c0x + 1) + 3) + 3)/(-1(-2sin(3\u03c0x + 1) + 3) + 2)) + 1| - 2 and g(x) = -1(3x)^2 - 2(3x) + 4 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) = (2(-2(3sin(1\u03c0x + 3) - 1) + 2) - 2)/(1(-2(3sin(1\u03c0x + 3) - 1) + 2) - 3), g(x) = 2|(-2sin(1\u03c0x + 3) + 2) + 1| + 1, x = 1.0, 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": "4.9", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3sin(2\u03c0(4((-1x + 3)/(2x - 3)) + 5) - 1) + 3 and g(x) = 2|(-3x + 4) + 1| - 3 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -5((3(-3|(1x^2 - 4x - 5) - 1| + 1) - 1)/(-1(-3|(1x^2 - 4x - 5) - 1| + 1) - 1)), g(x) = -3|(-5(2cos(1\u03c0x + 1) + 1) - 4) + 2| + 1, x = -1.2, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3(3sin(1\u03c0((2x)/(1x + 1)) - 1)) - 4 and g(x) = (1(-3x^2 - 3x + 4) - 2)/(-1(-3x^2 - 3x + 4) + 2) from x = -0.9 to x = -0.8. 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((2(-2|x + 2| + 3) + 1)/(2(-2|x + 2| + 3))) - 5 and g(x) = 1cos(1\u03c0(-4x + 1) - 3) + 1 from x = -2.8 to 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": "Calculate the area enclosed between the functions f(x) = 1(-4(-2|x - 2| - 2)^2) + 1 and g(x) = -2e^(-2((2x + 3)/(-2x - 2))) - 3 from x = 1.7 to x = 2.2. 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": "Find the area of the region bounded by the curves f(x) = (-2(4(-1x - 3)^2 - 4(-1x - 3)) - 1)/(-1(4(-1x - 3)^2 - 4(-1x - 3)) + 2), g(x) = -3(-3cos(3\u03c0x + 2) - 3) + 2, x = 4.1, and x = 4.199999999999999. 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(2|(-1e^(1x) - 1) - 2| - 3) - 1)/(-2(2|(-1e^(1x) - 1) - 2| - 3) - 3) and g(x) = -3|(-3sin(2\u03c0x + 1) + 2)| 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1(2|(-5x^2 - 3x + 4) + 1| - 1) - 2 and g(x) = 2sin(1\u03c0(5x - 5) - 3) + 3 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": "4.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(3((2x + 2)/(2x + 3))^2 + 1) + 1, g(x) = -1e^(1(-1x + 2)) - 3, 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": "25.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-3|(-3sin(1\u03c0x + 1) + 3) + 3| + 3) - 5 and g(x) = 2|(-2cos(2\u03c0x + 3) - 2) - 2| + 3 between the vertical lines x = 3.5 and x = 4.7. 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(-5(2cos(2\u03c0((3x + 2)/(1x + 3)) - 2) + 1)^2 + 3(2cos(2\u03c0((3x + 2)/(1x + 3)) - 2) + 1)) - 4 and g(x) = 2e^(-2(1((2x - 2)/(1x + 1))^2 - 2((2x - 2)/(1x + 1)) + 3)) - 2 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": "1.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1((-2(-2(-2|x - 2| + 2) - 1))/(-1(-2(-2|x - 2| + 2) - 1) - 1))^2 + 5((-2(-2(-2|x - 2| + 2) - 1))/(-1(-2(-2|x - 2| + 2) - 1) - 1)) + 4, g(x) = (-3(-2|(-4x + 1) - 1| + 2) + 2)/(-2(-2|(-4x + 1) - 1| + 2) - 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": "8.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(3\u03c0(-2|((3x + 3)/(2x - 1)) + 2| - 1) + 1), g(x) = 2sin(2\u03c0(1|x| + 3) + 1), 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-1e^(-1(-2|x| + 1)) + 2) - 1)/(-1(-1e^(-1(-2|x| + 1)) + 2) + 2), g(x) = (1(1x - 3) + 3)/(2(1x - 3) + 3), x = 0.8, 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": "31.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -1(2|(1sin(3\u03c0x - 1) - 1)|)^2 - 1(2|(1sin(3\u03c0x - 1) - 1)|) + 2, g(x) = 1e^(-1(3|x + 3| - 3)) - 3, 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": "3.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2(2cos(2\u03c0((1(-2|x + 3| + 2) - 2)/(1(-2|x + 3| + 2) - 3)) - 1) + 1) - 3, g(x) = 2(-4(-2e^(1x) + 3) - 1)^2 + 3(-4(-2e^(1x) + 3) - 1) - 5, 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": "Find the area of the region bounded by the curves f(x) = 2(-1|(5(2sin(1\u03c0x + 3) - 3) - 2) + 2| + 2)^2 - 5(-1|(5(2sin(1\u03c0x + 3) - 3) - 2) + 2| + 2), g(x) = 5((-3(4x - 1) - 3)/(3(4x - 1) - 1))^2 + 1((-3(4x - 1) - 3)/(3(4x - 1) - 1)) - 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": "-63.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1(-2sin(1\u03c0(-2x - 2) - 3) + 2)^2 + 2(-2sin(1\u03c0(-2x - 2) - 3) + 2) - 1, g(x) = (-3(-2|x + 2| + 1))/(-1(-2|x + 2| + 1) + 3), x = 2.4, 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": "7.6", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3(-5((-1x - 1)/(-1x)) - 5)^2 + 1(-5((-1x - 1)/(-1x)) - 5) - 3 and g(x) = 3(1|x - 2| - 3) - 2 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 4(3(-2|((-3x + 3)/(3x - 1)) - 2| + 2)^2 + 5(-2|((-3x + 3)/(3x - 1)) - 2| + 2) - 1) + 5 and g(x) = -1e^(-1(1|((2x - 2)/(1x + 1)) + 1| - 1)) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3((3(5(-3|x - 1|) + 1) + 2)/(-1(5(-3|x - 1|) + 1) - 3))^2 + 4((3(5(-3|x - 1|) + 1) + 2)/(-1(5(-3|x - 1|) + 1) - 3)) + 4 and g(x) = -4(-3cos(2\u03c0((1x - 1)/(-1x - 2)) + 3) + 1) - 3 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": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-2e^(1((-1(3|x + 3| + 1) - 2)/(-2(3|x + 3| + 1) - 2))) + 1)^2 + 2(-2e^(1((-1(3|x + 3| + 1) - 2)/(-2(3|x + 3| + 1) - 2))) + 1) + 5 and g(x) = (2(2sin(2\u03c0(4x^2 + 1x + 1) - 3) + 1) - 3)/(-1(2sin(2\u03c0(4x^2 + 1x + 1) - 3) + 1) + 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": "1.1", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -2((1(-1|x + 3| + 3) - 1)/(-1(-1|x + 3| + 3) - 3)) + 3 and g(x) = -4(3|x + 2| - 2) from x = -2.4 to x = -1.6. 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(1sin(2\u03c0(1x + 1) + 3) + 3)^2 + 4(1sin(2\u03c0(1x + 1) + 3) + 3) - 5, g(x) = (3(-1cos(1\u03c0x)) - 1)/(-1(-1cos(1\u03c0x))), x = 1.5, 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": "34.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2|(2e^(1((1(-5x^2 + 4x - 3) + 3)/(-3(-5x^2 + 4x - 3) + 2))) - 1) + 1| + 1, g(x) = -1|(1(-3x - 1)^2 + 2(-3x - 1) + 2) - 3| + 3, 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": "7.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (1(-2(2|x - 3| - 3)^2 - 3(2|x - 3| - 3) + 5) - 2)/(-3(-2(2|x - 3| - 3)^2 - 3(2|x - 3| - 3) + 5) + 1) and g(x) = 5(1|x + 2| + 3) + 2 between the vertical lines x = 1.0 and x = 2.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -3|(1(2cos(2\u03c0(1x^2 + 3x + 1) - 1) - 2) + 4) - 2| + 3 and g(x) = (1(-3(-3cos(2\u03c0x - 2) + 3) - 3) - 2)/(1(-3(-3cos(2\u03c0x - 2) + 3) - 3) + 1) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-3(-5(1|(2e^(1x)) + 3| + 3)^2 + 2(1|(2e^(1x)) + 3| + 3) - 5) + 3)/(1(-5(1|(2e^(1x)) + 3| + 3)^2 + 2(1|(2e^(1x)) + 3| + 3) - 5)) and g(x) = -2|((-1(-4x + 1) - 2)/(2(-4x + 1) + 2)) - 2| + 1 from x = 0.5 to x = 0.8. 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) = -3|(1((1x - 2)/(1x - 3))^2 + 1((1x - 2)/(1x - 3)) + 1) - 1| + 3, g(x) = 1(-5x + 4)^2 + 2(-5x + 4) - 4, x = 0.6, 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": "3.7", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(1sin(3\u03c0(-2(5x - 4)^2 - 5(5x - 4) + 2) - 2)) - 2| - 2, g(x) = -3cos(2\u03c0(-1|(1x^2 - 4x - 4) + 1| + 1) + 2), x = -4.8, 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -1(1|((1x + 2)/(-1x)) + 3| - 3)^2 + 3(1|((1x + 2)/(-1x)) + 3| - 3) + 5 and g(x) = -4(3cos(2\u03c0x - 3) - 3) + 4 from x = -1.6 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) = -5((3(3cos(1\u03c0(2|x - 3| + 3) + 1)))/(3(3cos(1\u03c0(2|x - 3| + 3) + 1)) + 3)) + 2, g(x) = -2(-3|((-2x - 2)/(-3x - 3)) - 2| + 2), x = -0.1, 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": "11.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = -4(-3sin(1\u03c0(-3|x - 2| + 2) + 3)) + 5 and g(x) = (-1(1cos(1\u03c0x - 2) + 3) - 1)/(3(1cos(1\u03c0x - 2) + 3)) from x = -2.6 to x = -2.4. 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": "Find the area of the region bounded by the curves f(x) = -2(1e^(-1((-1x + 2)/(-3x + 4))) + 2)^2 + 4(1e^(-1((-1x + 2)/(-3x + 4))) + 2) - 4, g(x) = -3|(-3sin(2\u03c0x - 1) - 1) - 2| - 2, x = 2.7, 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": "1.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3cos(2\u03c0((3(3|x - 1| - 2) - 1)/(2(3|x - 1| - 2) + 1))) and g(x) = -3(1|x| + 1) + 1 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (-1(-3(3|(-3x^2 - 4x + 1) + 3| - 2)) - 2)/(-2(-3(3|(-3x^2 - 4x + 1) + 3| - 2)) + 1) and g(x) = -2(2|((2x)/(-3x + 1)) + 2|) - 5 from x = -2.1 to x = 0.6. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4((2(1|(4x - 1) + 3|))/(2(1|(4x - 1) + 3|) - 1))^2 + 5 and g(x) = 1((-2(2x - 2) - 2)/(-3(2x - 2)))^2 + 4((-2(2x - 2) - 2)/(-3(2x - 2))) + 1 between the vertical lines x = 1.0 and x = 1.4. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -5(-3(2sin(2\u03c0x + 3) - 2) - 4)^2 - 5(-3(2sin(2\u03c0x + 3) - 2) - 4) - 2 and g(x) = -2(1e^(-1x) - 3) - 2 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3sin(1\u03c0(1|((-2x + 3)/(-2x - 2)) - 3| - 3) - 2) - 2 and g(x) = 2sin(2\u03c0(1x - 5) + 3) 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 2(3((3(3sin(3\u03c0x + 1)) - 3)/(-2(3sin(3\u03c0x + 1)) + 3))^2 + 3((3(3sin(3\u03c0x + 1)) - 3)/(-2(3sin(3\u03c0x + 1)) + 3)) + 2) - 4 and g(x) = (-2(-2|(3x^2 + 2x)| - 2))/(-3(-2|(3x^2 + 2x)| - 2) - 2) 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4((2(1cos(2\u03c0(-4x)) - 1))/(-1(1cos(2\u03c0(-4x)) - 1) - 3))^2 - 5((2(1cos(2\u03c0(-4x)) - 1))/(-1(1cos(2\u03c0(-4x)) - 1) - 3)) - 1, g(x) = -5((-3(3sin(3\u03c0x + 2) + 2) - 1)/(-3(3sin(3\u03c0x + 2) + 2) - 2)) - 4, 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": "0.6", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -4(-2|((2x + 1)/(-2x - 2))| + 2) + 3, g(x) = -1(-2e^(1x) + 2)^2 - 5(-2e^(1x) + 2) - 3, x = 0.3, 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": "1.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -2sin(3\u03c0(-3(-2|((1x)/(-3x - 2)) - 1| - 1)^2 - 3(-2|((1x)/(-3x - 2)) - 1| - 1)) - 3) - 3, g(x) = 1(4((3x + 2)/(1x)) + 5)^2 - 2(4((3x + 2)/(1x)) + 5) - 5, x = -0.5, 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": "0.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 3((2(1|x + 1| - 3) + 1)/(1(1|x + 1| - 3)))^2 + 5((2(1|x + 1| - 3) + 1)/(1(1|x + 1| - 3))) + 3 and g(x) = 4(2|x + 2|) - 2 from x = -3.8 to x = -3.2. 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": "Calculate the area enclosed between the functions f(x) = 5((-2(1(1|x| - 1) + 4) + 3)/(-2(1(1|x| - 1) + 4) + 1))^2 - 3((-2(1(1|x| - 1) + 4) + 3)/(-2(1(1|x| - 1) + 4) + 1)) - 3 and g(x) = 1|((-1(2cos(3\u03c0x - 1)) + 1)/(2(2cos(3\u03c0x - 1)) - 1)) + 2| - 2 from x = 4.6 to x = 4.9. 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": "Calculate the area enclosed between the functions f(x) = 1(1((2(-3sin(2\u03c0x + 1) - 2))/(-1(-3sin(2\u03c0x + 1) - 2) + 3)) - 3)^2 + 5(1((2(-3sin(2\u03c0x + 1) - 2))/(-1(-3sin(2\u03c0x + 1) - 2) + 3)) - 3) - 2 and g(x) = (2(2|(4x^2 - 3x - 2) - 2| - 2))/(2(2|(4x^2 - 3x - 2) - 2| - 2) - 3) 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": "4.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1(2|(2x + 3) + 1| - 2)^2 - 1(2|(2x + 3) + 1| - 2) + 2 and g(x) = 1cos(2\u03c0(-3x^2 - 4x - 5) + 3) + 3 between the vertical lines x = -1.6 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": "Find the area of the region bounded by the curves f(x) = 2|((-2(4(-4x - 5)^2 - 3(-4x - 5) - 3) - 1)/(1(4(-4x - 5)^2 - 3(-4x - 5) - 3))) - 1| - 3, g(x) = (1(1|(-3x + 2) - 1| + 2) + 3)/(-3(1|(-3x + 2) - 1| + 2) - 1), 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2(1|((2(1e^(2x) - 3) + 1)/(-2(1e^(2x) - 3) - 3)) + 2| + 1) + 2, g(x) = 3((2(2|x - 1| - 2) - 1)/(1(2|x - 1| - 2) - 3))^2 - 5((2(2|x - 1| - 2) - 1)/(1(2|x - 1| - 2) - 3)) - 4, x = -0.7, 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": "47.4", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = (1(2(-3|(-3e^(2x) + 1) - 3| - 3) + 2) - 2)/(3(2(-3|(-3e^(2x) + 1) - 3| - 3) + 2) - 2) and g(x) = 1|(2(-4x - 1)^2 + 3(-4x - 1) - 2) - 3| - 2 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (3(-3(1|x + 3| - 1)^2 + 5(1|x + 3| - 1) + 2) + 2)/(-1(-3(1|x + 3| - 1)^2 + 5(1|x + 3| - 1) + 2) - 1) and g(x) = -2|(-2x + 2) + 1| - 3 between the vertical lines x = -3.5 and x = -2.5. 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": "Determine the area of the region enclosed by the graphs of f(x) = 2cos(1\u03c0(-2|(-3x^2 + 4x + 2) + 2| - 2) - 3) - 1 and g(x) = 3|(-3cos(1\u03c0x - 3))| - 3 between the vertical lines x = -3.7 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": "Calculate the area enclosed between the functions f(x) = 2|(1cos(3\u03c0((3x + 3)/(-1x + 2)) - 2) + 1) + 1| - 1 and g(x) = (-2(2|x + 2| - 1) - 2)/(3(2|x + 2| - 1) + 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) = -4(1(2|x| + 1)^2 - 2(2|x| + 1) - 1) and g(x) = -1(1e^(-2x) - 2)^2 + 4(1e^(-2x) - 2) - 1 between the vertical lines x = -1.0 and x = -0.6. 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": "Find the area of the region bounded by the curves f(x) = -2cos(2\u03c0(1|(1x^2 - 5x + 5) + 2| + 3) + 3) + 3, g(x) = (-2(-3x + 3) - 2)/(-1(-3x + 3) + 3), x = 3.4, 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": "0.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(2((2x - 1)/(2x)) + 3) + 1| + 2, g(x) = (2(2|x + 2| - 2) - 2)/(2(2|x + 2| - 2) + 3), 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": "2.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((1(-2|x - 2| - 2))/(-2(-2|x - 2| - 2) - 3))^2 - 2, g(x) = (-3(1cos(3\u03c0x + 1) + 1) - 3)/(-3(1cos(3\u03c0x + 1) + 1) + 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|(-1((-1x + 1)/(-2x)) + 4) - 2| + 3 and g(x) = 2|(1x^2 - 5x - 4) - 3| 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 4(-2((-2(1sin(3\u03c0x + 1) - 2) + 2)/(-1(1sin(3\u03c0x + 1) - 2) - 3)) + 1)^2 + 4(-2((-2(1sin(3\u03c0x + 1) - 2) + 2)/(-1(1sin(3\u03c0x + 1) - 2) - 3)) + 1) - 1 and g(x) = 2(3(2|x - 3| - 1)^2 + 2) - 3 between the vertical lines x = -1.4 and x = -1.2. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2(2cos(3\u03c0((3(3|x| + 1) - 1)/(-3(3|x| + 1) + 2)) - 3) - 1) + 3 and g(x) = 2(-1|(-1x + 5) - 2| - 1)^2 - 3(-1|(-1x + 5) - 2| - 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-3(3|(5x^2 - 3x - 2) + 2|) + 2)/(-2(3|(5x^2 - 3x - 2) + 2|) + 1), g(x) = 3(-3x)^2 + 2(-3x) + 4, 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": "1.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2|((2(-2x^2 + 1x + 5) - 1)/(-2(-2x^2 + 1x + 5) + 3)) - 2| - 2 and g(x) = -1e^(1(-1x^2 - 3x)) between the vertical lines x = -2.0 and x = -1.1. 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) = -2sin(2\u03c0(-2|((-1(4x + 1) - 1)/(-3(4x + 1) - 2)) + 3| + 2) - 1) + 1, g(x) = 2e^(2(-2|(-1x^2 - 5x - 5)| - 1)) - 1, x = -0.4, and x = -0.30000000000000004. 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|(-4((3x - 2)/(-1x - 1))^2 + 5((3x - 2)/(-1x - 1)) - 3) + 2| and g(x) = -1(-1e^(2x))^2 - 2(-1e^(2x)) + 5 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": "2.1", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 3cos(2\u03c0((-3(-1x^2 + 3) + 2)/(-3(-1x^2 + 3) - 1)) - 3) - 2 and g(x) = (1(1x - 4))/(3(1x - 4) - 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": "0.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -3(5((3(-3cos(1\u03c0x + 2) + 1))/(-1(-3cos(1\u03c0x + 2) + 1) + 2))^2 - 4((3(-3cos(1\u03c0x + 2) + 1))/(-1(-3cos(1\u03c0x + 2) + 1) + 2))) + 3 and g(x) = (1(-1e^(2(-4x^2 - 2x)) - 1) - 1)/(-1(-1e^(2(-4x^2 - 2x)) - 1) - 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": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 4((1(2|(-2cos(1\u03c0x + 2) - 2) + 3| + 1) - 2)/(1(2|(-2cos(1\u03c0x + 2) - 2) + 3| + 1) + 2))^2 + 4((1(2|(-2cos(1\u03c0x + 2) - 2) + 3| + 1) - 2)/(1(2|(-2cos(1\u03c0x + 2) - 2) + 3| + 1) + 2)) + 4, g(x) = 2e^(-1((1(-1|x + 1| - 1) - 2)/(3(-1|x + 1| - 1)))) + 2, x = 1.7, 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -4((1(-2|x + 2|))/(-2(-2|x + 2|)))^2 - 1((1(-2|x + 2|))/(-2(-2|x + 2|))) + 1 and g(x) = (1(2cos(3\u03c0x + 1) + 1))/(-3(2cos(3\u03c0x + 1) + 1) - 1) between the vertical lines x = -0.3 and x = 0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0.3", "dataset": "MATH"}
{"messages": [{"content": "Calculate the area enclosed between the functions f(x) = 1|(-5(-1(-3sin(1\u03c0x + 1) + 3)^2 + 4(-3sin(1\u03c0x + 1) + 3) - 5)) + 3| - 2 and g(x) = -5((-3(-2|x - 3| + 3) + 3)/(3(-2|x - 3| + 3) - 2)) + 5 from x = 2.7 to x = 3.7. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-3e^(2(3x - 5)) + 2) - 1)/(3(-3e^(2(3x - 5)) + 2)) and g(x) = -1(-1x - 4)^2 - 3(-1x - 4) + 2 between the vertical lines x = -0.2 and x = 1.6. 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": "Determine the area of the region enclosed by the graphs of f(x) = 5((-3(-4x^2 - 3x + 4) - 2)/(-2(-4x^2 - 3x + 4) - 2)) - 1 and g(x) = 2(-4x^2 - 3x - 2) + 2 between the vertical lines x = -1.5 and x = 0.8. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22.7", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(1(1|(-3x - 1) + 2| - 2)^2 - 1(1|(-3x - 1) + 2| - 2) - 3) - 2)/(1(1(1|(-3x - 1) + 2| - 2)^2 - 1(1|(-3x - 1) + 2| - 2) - 3) + 2) and g(x) = 4(-1|((-3x + 1)/(1x)) + 3| - 3) between the vertical lines x = -0.8 and x = -0.1. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 2|(-1(3((-3x + 2)/(2x))^2 - 4((-3x + 2)/(2x)) + 2) - 5) - 3| - 3, g(x) = (-3(2|(-2x^2 + 4x + 4) + 1| + 1) + 2)/(-1(2|(-2x^2 + 4x + 4) + 1| + 1) + 3), 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": "39.4", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1((-1(-3|x - 1| + 3) + 3)/(-2(-3|x - 1| + 3) - 1))^2 + 2((-1(-3|x - 1| + 3) + 3)/(-2(-3|x - 1| + 3) - 1)) - 1 and g(x) = 2(-2sin(2\u03c0x + 3) - 3)^2 + 1(-2sin(2\u03c0x + 3) - 3) + 2 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": "47.6", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = (-3(-1(-1(2sin(3\u03c0x + 3) - 1)^2 - 4(2sin(3\u03c0x + 3) - 1) + 3) - 1) + 2)/(1(-1(-1(2sin(3\u03c0x + 3) - 1)^2 - 4(2sin(3\u03c0x + 3) - 1) + 3) - 1)) and g(x) = 2|(-1((-2x + 3)/(-2x - 3))^2 - 3((-2x + 3)/(-2x - 3)) + 4) - 3| + 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": "1.5", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(-3|x + 3| + 2) + 2)^2 + 3(-1(-3|x + 3| + 2) + 2) - 1 and g(x) = (-1(1|x - 3| + 3) + 1)/(1(1|x - 3| + 3)) between the vertical lines x = -4.0 and x = -3.0. 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) = -1|((2(-1(4x^2 - 2x + 4) - 4) + 3)/(3(-1(4x^2 - 2x + 4) - 4) - 2)) - 2| + 3, g(x) = 3e^(1((-1(-4x^2 + 4x + 2))/(-3(-4x^2 + 4x + 2) - 2))), 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": "4.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1|(-4(-5x^2 + 5x) + 3) - 2|, g(x) = -3cos(2\u03c0(-1|x + 2| - 3) - 2) - 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": "0.0", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -1(-1(2|x + 1| - 1) - 1)^2 - 5(-1(2|x + 1| - 1) - 1) + 2 and g(x) = 4((-3x - 2)/(-1x + 2))^2 - 2((-3x - 2)/(-1x + 2)) - 5 between the vertical lines x = -3.5 and x = 0.3. Round to 1 decimal place.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 5(-2e^(2(3|((-2x - 2)/(-1x)) + 1| - 2)) + 1) - 3 and g(x) = 3cos(1\u03c0(5((-3x + 3)/(2x + 1))^2 + 3((-3x + 3)/(2x + 1)) - 4) + 3) - 3 between the vertical lines x = -0.8 and x = -0.7000000000000001. 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((-1(-2(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) + 4))/(-1(-2(-2|x - 1| - 1)^2 - 1(-2|x - 1| - 1) + 4) + 3)) + 5 and g(x) = -2cos(1\u03c0((-3(4x + 4) - 3)/(-3(4x + 4) + 1)) - 3) + 1 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": "21.0", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(2(-3(-1|x - 3| + 3))^2 + 3(-3(-1|x - 3| + 3)) - 1) + 2)/(-1(2(-3(-1|x - 3| + 3))^2 + 3(-3(-1|x - 3| + 3)) - 1) + 2), g(x) = (2(-1(-3|x - 1| - 1)^2 - 4(-3|x - 1| - 1) + 1) - 1)/(-1(-1(-3|x - 1| - 1)^2 - 4(-3|x - 1| - 1) + 1) + 2), x = -0.0, 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": "18.8", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = 1cos(3\u03c0(-5(-3((-3x - 1)/(-2x - 3))^2 - 1) - 1) - 1) - 3, g(x) = -2sin(3\u03c0(1|(-5x - 4) - 3| - 3) - 1) - 1, 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": "0.5", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = -3cos(2\u03c0(-2((-1x - 1)/(-2x - 3))^2 - 4((-1x - 1)/(-2x - 3)) - 3) - 2), g(x) = -2(3|x + 1| - 3)^2 - 4(3|x + 1| - 3) - 4, 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": "Determine the area of the region enclosed by the graphs of f(x) = -2(2cos(1\u03c0(-1|((1x - 2)/(-3x - 3)) + 1|) + 1) - 3)^2 - 4(2cos(1\u03c0(-1|((1x - 2)/(-3x - 3)) + 1|) + 1) - 3) + 3 and g(x) = 2(1cos(3\u03c0((2x - 2)/(-2x + 1)) - 1) + 2)^2 - 5(1cos(3\u03c0((2x - 2)/(-2x + 1)) - 1) + 2) + 1 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": "0.9", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 2sin(3\u03c0(4(-5(-1|x - 3| - 3) + 5)^2 + 1(-5(-1|x - 3| - 3) + 5)) - 1) and g(x) = 2(3e^(2((-1x + 1)/(2x - 3))) - 2) - 4 between the vertical lines x = 1.1 and x = 1.2000000000000002. 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(-1(-3sin(1\u03c0x + 1)) + 3)^2 - 1(-1(-3sin(1\u03c0x + 1)) + 3) - 1 and g(x) = -2cos(1\u03c0((3x + 3)/(1x + 3)) + 2) - 2 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": "0.1", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (-2(-4(3x^2 - 5x + 2) + 3))/(-2(-4(3x^2 - 5x + 2) + 3) - 1), g(x) = -1((-1x - 3)/(3x + 3)) + 1, x = 0.2, 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": "2.8", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = 1e^(1(-1(1((-3x - 2)/(3x + 2))^2 - 4((-3x - 2)/(3x + 2)) + 1) + 5)) - 1 and g(x) = -2sin(2\u03c0(5((3x + 1)/(-3x + 2))^2 + 3((3x + 1)/(-3x + 2)) + 2)) between the vertical lines x = 1.8 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": "Find the area of the region bounded by the curves f(x) = 1|((-2(5x - 3) - 3)/(2(5x - 3) + 2)) + 3| - 2, g(x) = -2(-2x + 1)^2 + 4(-2x + 1) - 2, 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": "2.2", "dataset": "MATH"}
{"messages": [{"content": "Determine the area of the region enclosed by the graphs of f(x) = -2(-1|((2x - 2)/(-3x - 2)) + 1| - 2)^2 - 3(-1|((2x - 2)/(-3x - 2)) + 1| - 2) - 3 and g(x) = -3(-2cos(1\u03c0x - 3) - 1)^2 - 2(-2cos(1\u03c0x - 3) - 1) - 5 between the vertical lines x = 3.4 and x = 3.8. 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": "Find the area of the region bounded by the curves f(x) = 3cos(3\u03c0(-1((3x)/(-1x))^2 - 3((3x)/(-1x)) + 5) + 2), g(x) = 3|(3x) + 3| - 1, x = -1.2, 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": "Find the area of the region bounded by the curves f(x) = -3(1(2sin(2\u03c0(-1|x - 1| + 2) + 2) + 2) - 5)^2 + 1(1(2sin(2\u03c0(-1|x - 1| + 2) + 2) + 2) - 5) - 5, g(x) = 3(2((1x + 1)/(-1x + 2))^2 + 5((1x + 1)/(-1x + 2)) - 5) + 5, x = -2.0, 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": "29.4", "dataset": "MATH"}
{"messages": [{"content": "Find the area of the region bounded by the curves f(x) = (3(1(-1|x - 3| + 3) + 5) - 1)/(-1(1(-1|x - 3| + 3) + 5) + 3), g(x) = -2|(3sin(1\u03c0x + 3) - 2) - 3| + 3, x = 1.9, 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": "6.3", "dataset": "MATH"}