{"messages": [{"content": "For the function f(x) = -2(4(-1|(-5(3sin(1\u03c0((2x - 1)/(3x + 3)) - 2) + 3)^2 + 1) + 3| - 2)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(3sin(1\u03c0(1|((2(2|((-1x - 1)/(1x - 2)) + 1| - 2) + 2)/(3(2|((-1x - 1)/(1x - 2)) + 1| - 2) - 1))| - 1) - 3) + 2) - 3)/(-3(3sin(1\u03c0(1|((2(2|((-1x - 1)/(1x - 2)) + 1| - 2) + 2)/(3(2|((-1x - 1)/(1x - 2)) + 1| - 2) - 1))| - 1) - 3) + 2) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(3|(1(-4((2(3cos(1\u03c0x - 2) - 3) - 2)/(1(3cos(1\u03c0x - 2) - 3))) - 1) + 5) - 1| - 1) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((1(5((3(3(2cos(2\u03c0x + 2) - 2) + 2) + 3)/(2(3(2cos(2\u03c0x + 2) - 2) + 2) - 1))^2 - 4((3(3(2cos(2\u03c0x + 2) - 2) + 2) + 3)/(2(3(2cos(2\u03c0x + 2) - 2) + 2) - 1)) - 1) + 2)/(2(5((3(3(2cos(2\u03c0x + 2) - 2) + 2) + 3)/(2(3(2cos(2\u03c0x + 2) - 2) + 2) - 1))^2 - 4((3(3(2cos(2\u03c0x + 2) - 2) + 2) + 3)/(2(3(2cos(2\u03c0x + 2) - 2) + 2) - 1)) - 1) + 1)) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(5((2(-1|(3(3sin(2\u03c0x + 1) + 3)^2 + 1(3sin(2\u03c0x + 1) + 3) + 3) - 2| + 3) - 1)/(3(-1|(3(3sin(2\u03c0x + 1) + 3)^2 + 1(3sin(2\u03c0x + 1) + 3) + 3) - 2| + 3) - 2)) - 1)^2 + 2(5((2(-1|(3(3sin(2\u03c0x + 1) + 3)^2 + 1(3sin(2\u03c0x + 1) + 3) + 3) - 2| + 3) - 1)/(3(-1|(3(3sin(2\u03c0x + 1) + 3)^2 + 1(3sin(2\u03c0x + 1) + 3) + 3) - 2| + 3) - 2)) - 1) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(2|(-1(1(-1(-1sin(1\u03c0x) + 3)^2 + 2(-1sin(1\u03c0x) + 3) - 2)) + 4) + 1| + 1) - 1| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(2|(-3cos(1\u03c0(-3(3(-1x^2 - 5x - 5) - 1)^2 + 5(3(-1x^2 - 5x - 5) - 1) + 2) + 1) - 1)| - 1) + 3| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-3(-1((1(-3(-1cos(1\u03c0((1x - 2)/(2x - 1)) - 3) - 3) - 1) + 2)/(3(-3(-1cos(1\u03c0((1x - 2)/(2x - 1)) - 3) - 3) - 1) + 1)) + 2))/(2(-1((1(-3(-1cos(1\u03c0((1x - 2)/(2x - 1)) - 3) - 3) - 1) + 2)/(3(-3(-1cos(1\u03c0((1x - 2)/(2x - 1)) - 3) - 3) - 1) + 1)) + 2) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-1(-5((3(-2((1x - 1)/(-3x - 3)) + 5) + 3)/(1(-2((1x - 1)/(-3x - 3)) + 5) + 1)) + 5)^2 + 4(-5((3(-2((1x - 1)/(-3x - 3)) + 5) + 3)/(1(-2((1x - 1)/(-3x - 3)) + 5) + 1)) + 5) - 5)^2 + 2(-1(-5((3(-2((1x - 1)/(-3x - 3)) + 5) + 3)/(1(-2((1x - 1)/(-3x - 3)) + 5) + 1)) + 5)^2 + 4(-5((3(-2((1x - 1)/(-3x - 3)) + 5) + 3)/(1(-2((1x - 1)/(-3x - 3)) + 5) + 1)) + 5) - 5) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(-1|(3((1(-1(3sin(1\u03c0x - 1) + 2) + 4) + 2)/(-1(-1(3sin(1\u03c0x - 1) + 2) + 4))) + 2) + 1| + 1) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((3(2cos(3\u03c0(1(5((-1x + 1)/(2x)) - 4)) + 3)) + 1)/(-3(2cos(3\u03c0(1(5((-1x + 1)/(2x)) - 4)) + 3)) + 1)) + 2| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(4(2((2(2(1cos(3\u03c0x - 3) + 3) - 1) + 1)/(-2(2(1cos(3\u03c0x - 3) + 3) - 1) - 3))) - 1)| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((2(-2(2(-3cos(3\u03c0((-2x + 3)/(2x - 1)) - 1) - 2) + 2)^2 - 4) - 1)/(1(-2(2(-3cos(3\u03c0((-2x + 3)/(2x - 1)) - 1) - 2) + 2)^2 - 4) + 2))^2 + 1((2(-2(2(-3cos(3\u03c0((-2x + 3)/(2x - 1)) - 1) - 2) + 2)^2 - 4) - 1)/(1(-2(2(-3cos(3\u03c0((-2x + 3)/(2x - 1)) - 1) - 2) + 2)^2 - 4) + 2)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|((-2(3sin(3\u03c0((1(1(-1x^2 + 2x + 5) + 2))/(1(1(-1x^2 + 2x + 5) + 2) - 2)) - 3) - 1) - 1)/(2(3sin(3\u03c0((1(1(-1x^2 + 2x + 5) + 2))/(1(1(-1x^2 + 2x + 5) + 2) - 2)) - 3) - 1) + 2))| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-3(3|(-1|(1cos(3\u03c0((-3x + 1)/(2x - 3)) - 2) + 3) + 1| + 2) - 2| + 3)^2 - 2(3|(-1|(1cos(3\u03c0((-3x + 1)/(2x - 3)) - 2) + 3) + 1| + 2) - 2| + 3) - 4) + 1| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-1(-3((2((-2(-1x^2 + 3x + 5) - 3)/(-2(-1x^2 + 3x + 5) + 3)) + 1)/(1((-2(-1x^2 + 3x + 5) - 3)/(-2(-1x^2 + 3x + 5) + 3)) + 1))^2) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-3(1(-1cos(2\u03c0(1|(5x^2 + 5x + 1) + 1| - 3) - 2) - 2)^2 - 2(-1cos(2\u03c0(1|(5x^2 + 5x + 1) + 1| - 3) - 2) - 2) - 2)^2 - 3(1(-1cos(2\u03c0(1|(5x^2 + 5x + 1) + 1| - 3) - 2) - 2)^2 - 2(-1cos(2\u03c0(1|(5x^2 + 5x + 1) + 1| - 3) - 2) - 2) - 2) - 4) - 3| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(2|(-1(3|(1(1cos(2\u03c0x + 1) + 1)^2 - 3(1cos(2\u03c0x + 1) + 1) - 2) - 1| - 2) - 5)| + 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((-1(-2|(1(-1sin(1\u03c0(-2x + 2)) - 3)^2 + 3(-1sin(1\u03c0(-2x + 2)) - 3))| - 3) - 2)/(-3(-2|(1(-1sin(1\u03c0(-2x + 2)) - 3)^2 + 3(-1sin(1\u03c0(-2x + 2)) - 3))| - 3) - 1)) - 3| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(-2(-3|(4(-2(-2sin(1\u03c0x - 3) - 1)^2 - 3(-2sin(1\u03c0x - 3) - 1) + 3)^2 + 3(-2(-2sin(1\u03c0x - 3) - 1)^2 - 3(-2sin(1\u03c0x - 3) - 1) + 3) + 1) - 3| - 1) - 1) + 3| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2cos(1\u03c0(4(5((3(-5x) - 3)/(-1(-5x) - 2))^2 + 5((3(-5x) - 3)/(-1(-5x) - 2)) - 4)) - 1) + 1) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(-2|(1(4(2|(-3x^2 + 2x + 1) + 2| - 1)^2 - 3(2|(-3x^2 + 2x + 1) + 2| - 1)) + 1) - 3| - 1) + 1)/(-3(-2|(1(4(2|(-3x^2 + 2x + 1) + 2| - 1)^2 - 3(2|(-3x^2 + 2x + 1) + 2| - 1)) + 1) - 3| - 1) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3((-2(4(-2cos(1\u03c0(3|(-1x + 1) - 1|) + 3) - 1)) + 3)/(-2(4(-2cos(1\u03c0(3|(-1x + 1) - 1|) + 3) - 1))))^2 + 2((-2(4(-2cos(1\u03c0(3|(-1x + 1) - 1|) + 3) - 1)) + 3)/(-2(4(-2cos(1\u03c0(3|(-1x + 1) - 1|) + 3) - 1)))) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3((-3(-1(3sin(3\u03c0(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 3) + 3)/(-3(-1(3sin(3\u03c0(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 3)))^2 - 1((-3(-1(3sin(3\u03c0(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 3) + 3)/(-3(-1(3sin(3\u03c0(-1|((1x - 1)/(-3x - 3))| + 1) + 2)) + 3))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1sin(2\u03c0(3(4(4(1((-2x + 1)/(1x - 2))^2 - 3((-2x + 1)/(1x - 2)) + 1) - 1)) + 3) + 2) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2((-1(-1|((1(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 2)/(-3(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 1))| + 3) - 1)/(-1(-1|((1(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 2)/(-3(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 1))| + 3) + 2)) + 1)/(-3((-1(-1|((1(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 2)/(-3(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 1))| + 3) - 1)/(-1(-1|((1(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 2)/(-3(-3(-3sin(2\u03c0x + 2) - 3) - 3) - 1))| + 3) + 2)) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-2sin(2\u03c0((-1(-4((1(1x + 5) + 2)/(3(1x + 5) - 1))^2 + 5((1(1x + 5) + 2)/(3(1x + 5) - 1)) - 1) + 1)/(-2(-4((1(1x + 5) + 2)/(3(1x + 5) - 1))^2 + 5((1(1x + 5) + 2)/(3(1x + 5) - 1)) - 1) - 2)) - 2)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(3cos(3\u03c0(3(-5((-2(1x + 2) + 1)/(-2(1x + 2) + 3)) - 3)^2 - 1(-5((-2(1x + 2) + 1)/(-2(1x + 2) + 3)) - 3) - 2) + 1) - 1) + 1)/(3(3cos(3\u03c0(3(-5((-2(1x + 2) + 1)/(-2(1x + 2) + 3)) - 3)^2 - 1(-5((-2(1x + 2) + 1)/(-2(1x + 2) + 3)) - 3) - 2) + 1) - 1) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2((1((-2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 1)/(2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 3)) - 3)/(1((-2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 1)/(2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 3)) + 2))^2 - 5((1((-2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 1)/(2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 3)) - 3)/(1((-2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 1)/(2(-1cos(2\u03c0(-3|(-1x^2 - 3x + 2) - 1|) - 2) - 1) - 3)) + 2)) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(-2(-2|(-4(-3sin(1\u03c0(3|x + 1| - 1) - 2) + 2) + 2) - 2| + 1)^2 + 1(-2|(-4(-3sin(1\u03c0(3|x + 1| - 1) - 2) + 2) + 2) - 2| + 1) - 2) + 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-1(-2|((3(2sin(3\u03c0(2x + 3) - 1) - 1) + 3)/(2(2sin(3\u03c0(2x + 3) - 1) - 1))) - 2| + 3) - 3) + 1)/(-1(-1(-2|((3(2sin(3\u03c0(2x + 3) - 1) - 1) + 3)/(2(2sin(3\u03c0(2x + 3) - 1) - 1))) - 2| + 3) - 3) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5((-3(3(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1)^2 + 4(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1) + 5) - 2)/(3(3(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1)^2 + 4(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1) + 5) - 1))^2 - 2((-3(3(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1)^2 + 4(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1) + 5) - 2)/(3(3(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1)^2 + 4(-3|(2(-2x^2 - 2x + 4)^2 - 1(-2x^2 - 2x + 4) - 5) - 2| - 1) + 5) - 1)) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(-3|(-4(1(5((1x + 3)/(3x))^2 + 3((1x + 3)/(3x))) - 3)^2 + 3(1(5((1x + 3)/(3x))^2 + 3((1x + 3)/(3x))) - 3)) + 3|)^2 - 4(-3|(-4(1(5((1x + 3)/(3x))^2 + 3((1x + 3)/(3x))) - 3)^2 + 3(1(5((1x + 3)/(3x))^2 + 3((1x + 3)/(3x))) - 3)) + 3|), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((3(-1|(3|(1cos(3\u03c0((-2x - 2)/(-1x - 3))) + 3) + 1|)| + 3) + 3)/(2(-1|(3|(1cos(3\u03c0((-2x - 2)/(-1x - 3))) + 3) + 1|)| + 3) + 1)) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-2(-1|(1((1(2cos(3\u03c0x + 2)) + 3)/(-2(2cos(3\u03c0x + 2)) - 1))^2 - 1((1(2cos(3\u03c0x + 2)) + 3)/(-2(2cos(3\u03c0x + 2)) - 1)) + 1) + 3| + 1) + 4) + 2| + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3cos(2\u03c0(2(3(1|((2(5x - 3) - 2)/(1(5x - 3) - 2)) + 2| - 1) + 1) - 2) + 2) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(-3|(2|(2((3(-1cos(3\u03c0x - 3) + 3) + 3)/(2(-1cos(3\u03c0x - 3) + 3) - 3))^2 + 5((3(-1cos(3\u03c0x - 3) + 3) + 3)/(2(-1cos(3\u03c0x - 3) + 3) - 3)) + 5) + 1| + 3) - 3| + 1)| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(-4(2|((-2(-2sin(1\u03c0((-1x + 2)/(-1x - 3))) - 3) - 1)/(2(-2sin(1\u03c0((-1x + 2)/(-1x - 3))) - 3) + 2)) - 2| - 2) - 5) - 2)/(2(-4(2|((-2(-2sin(1\u03c0((-1x + 2)/(-1x - 3))) - 3) - 1)/(2(-2sin(1\u03c0((-1x + 2)/(-1x - 3))) - 3) + 2)) - 2| - 2) - 5) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|((2(1(-3cos(1\u03c0(-3(-3|x - 3| + 3)^2 - 4(-3|x - 3| + 3) - 5) - 2) - 2)^2 + 5) + 2)/(-3(1(-3cos(1\u03c0(-3(-3|x - 3| + 3)^2 - 4(-3|x - 3| + 3) - 5) - 2) - 2)^2 + 5) + 1)) + 1| + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(2cos(3\u03c0(4((3(-2(-1x - 3)^2 + 4(-1x - 3)) + 2)/(2(-2(-1x - 3)^2 + 4(-1x - 3)) - 1)) - 5) - 1) + 1)^2 - 3(2cos(3\u03c0(4((3(-2(-1x - 3)^2 + 4(-1x - 3)) + 2)/(2(-2(-1x - 3)^2 + 4(-1x - 3)) - 1)) - 5) - 1) + 1) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-1(-1(-3cos(2\u03c0(2((-1x + 2)/(-2x - 3))^2 - 1((-1x + 2)/(-2x - 3))) + 3) + 3) - 1)^2 + 2(-1(-3cos(2\u03c0(2((-1x + 2)/(-2x - 3))^2 - 1((-1x + 2)/(-2x - 3))) + 3) + 3) - 1) + 5) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1cos(3\u03c0(3|(-1(-1(-3(2|x - 3| + 1) + 5) - 2)^2 - 1(-1(-3(2|x - 3| + 1) + 5) - 2) + 1) + 1| - 1) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(2cos(2\u03c0(-2|((3(4((-2x + 3)/(3x - 2))^2 - 3((-2x + 3)/(3x - 2)) + 2) + 3)/(3(4((-2x + 3)/(3x - 2))^2 - 3((-2x + 3)/(3x - 2)) + 2) - 2)) - 1|))) - 3)/(-3(2cos(2\u03c0(-2|((3(4((-2x + 3)/(3x - 2))^2 - 3((-2x + 3)/(3x - 2)) + 2) + 3)/(3(4((-2x + 3)/(3x - 2))^2 - 3((-2x + 3)/(3x - 2)) + 2) - 2)) - 1|))) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((1(-5(1|(1(5x^2 - 2x - 2)^2 - 3(5x^2 - 2x - 2) - 4) + 2| - 3)^2 - 1(1|(1(5x^2 - 2x - 2)^2 - 3(5x^2 - 2x - 2) - 4) + 2| - 3) - 1))/(2(-5(1|(1(5x^2 - 2x - 2)^2 - 3(5x^2 - 2x - 2) - 4) + 2| - 3)^2 - 1(1|(1(5x^2 - 2x - 2)^2 - 3(5x^2 - 2x - 2) - 4) + 2| - 3) - 1) - 1))^2 - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(-3|(-5((2(-3sin(3\u03c0(1x^2 - 1x - 3)) - 2))/(-1(-3sin(3\u03c0(1x^2 - 1x - 3)) - 2) - 2))^2 - 5((2(-3sin(3\u03c0(1x^2 - 1x - 3)) - 2))/(-1(-3sin(3\u03c0(1x^2 - 1x - 3)) - 2) - 2)) + 5) + 3| + 3) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(3|((2(2(-2cos(1\u03c0(-1|x - 3| - 1)))^2 - 1(-2cos(1\u03c0(-1|x - 3| - 1))) + 1) + 3)/(2(2(-2cos(1\u03c0(-1|x - 3| - 1)))^2 - 1(-2cos(1\u03c0(-1|x - 3| - 1))) + 1) + 2)) + 2| - 3) - 2| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1(2(3cos(3\u03c0(-3|(3|x + 1| + 1) - 3| + 2) - 2)) - 4) + 2) - 3)/(-1(1(2(3cos(3\u03c0(-3|(3|x + 1| + 1) - 3| + 2) - 2)) - 4) + 2) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(-1cos(1\u03c0(2(4(-4(1x - 2)^2 + 2(1x - 2) + 2)^2 + 2(-4(1x - 2)^2 + 2(1x - 2) + 2) - 4) + 2)) + 2) + 3| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((1(-1|(-4(3|(-3cos(2\u03c0x - 3) + 2) - 2| + 1) + 2)| - 3) + 2)/(-3(-1|(-4(3|(-3cos(2\u03c0x - 3) + 2) - 2| + 1) + 2)| - 3) + 1)) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(1cos(3\u03c0(-3(-4((1((-3x + 3)/(2x - 1)) - 2)/(-2((-3x + 3)/(2x - 1)) + 1)) + 3) + 1)) - 3)^2 - 2(1cos(3\u03c0(-3(-4((1((-3x + 3)/(2x - 1)) - 2)/(-2((-3x + 3)/(2x - 1)) + 1)) + 3) + 1)) - 3) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(1|(1|(-1|(3sin(3\u03c0(1x - 2) + 2) + 3) + 2|) - 1| - 3) - 1| - 3)^2 - 2(1|(1|(-1|(3sin(3\u03c0(1x - 2) + 2) + 3) + 2|) - 1| - 3) - 1| - 3) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-2|(-2|(-1(2(-1cos(1\u03c0x - 2) + 3)^2 - 2(-1cos(1\u03c0x - 2) + 3) - 4)) + 3| + 2) - 1| + 3)| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(2(-3(1cos(3\u03c0(-3(1x + 4)^2 + 4(1x + 4) - 3) + 1) - 1)^2 + 5(1cos(3\u03c0(-3(1x + 4)^2 + 4(1x + 4) - 3) + 1) - 1))^2 + 4(-3(1cos(3\u03c0(-3(1x + 4)^2 + 4(1x + 4) - 3) + 1) - 1)^2 + 5(1cos(3\u03c0(-3(1x + 4)^2 + 4(1x + 4) - 3) + 1) - 1)) + 4) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-2|(2cos(1\u03c0(-4(5(-1x^2 - 3x + 1) - 5) - 3) - 3) - 1) + 1| - 3) - 3)/(2(-2|(2cos(1\u03c0(-4(5(-1x^2 - 3x + 1) - 5) - 3) - 3) - 1) + 1| - 3)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(-5(2(-2|(3sin(3\u03c0(1|x + 1|) + 3) - 2) - 2| + 1))^2 - 5(2(-2|(3sin(3\u03c0(1|x + 1|) + 3) - 2) - 2| + 1)) + 5))/(1(-5(2(-2|(3sin(3\u03c0(1|x + 1|) + 3) - 2) - 2| + 1))^2 - 5(2(-2|(3sin(3\u03c0(1|x + 1|) + 3) - 2) - 2| + 1)) + 5) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(-1(1sin(1\u03c0(-3(-1((1x + 3)/(-3x - 3)) + 4)^2 - 4(-1((1x + 3)/(-3x - 3)) + 4) + 5) - 2) + 2)^2 + 2(1sin(1\u03c0(-3(-1((1x + 3)/(-3x - 3)) + 4)^2 - 4(-1((1x + 3)/(-3x - 3)) + 4) + 5) - 2) + 2) + 5) - 2)/(1(-1(1sin(1\u03c0(-3(-1((1x + 3)/(-3x - 3)) + 4)^2 - 4(-1((1x + 3)/(-3x - 3)) + 4) + 5) - 2) + 2)^2 + 2(1sin(1\u03c0(-3(-1((1x + 3)/(-3x - 3)) + 4)^2 - 4(-1((1x + 3)/(-3x - 3)) + 4) + 5) - 2) + 2) + 5) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(-1(-3|(-3sin(1\u03c0((1((1x)/(-1x + 2)))/(-2((1x)/(-1x + 2)) - 1)) - 3) + 1) + 2| - 3) - 1) + 2)/(-2(-1(-3|(-3sin(1\u03c0((1((1x)/(-1x + 2)))/(-2((1x)/(-1x + 2)) - 1)) - 3) + 1) + 2| - 3) - 1) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((-1(-2|(-1|((1(-2cos(3\u03c0x - 3) - 1) - 3)/(1(-2cos(3\u03c0x - 3) - 1) - 2)) + 3| - 1) + 2| + 3) - 3)/(3(-2|(-1|((1(-2cos(3\u03c0x - 3) - 1) - 3)/(1(-2cos(3\u03c0x - 3) - 1) - 2)) + 3| - 1) + 2| + 3) + 3))^2 + 3((-1(-2|(-1|((1(-2cos(3\u03c0x - 3) - 1) - 3)/(1(-2cos(3\u03c0x - 3) - 1) - 2)) + 3| - 1) + 2| + 3) - 3)/(3(-2|(-1|((1(-2cos(3\u03c0x - 3) - 1) - 3)/(1(-2cos(3\u03c0x - 3) - 1) - 2)) + 3| - 1) + 2| + 3) + 3)) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(2|(-2(1(-1(1cos(1\u03c0x - 2) - 1)^2 - 4(1cos(1\u03c0x - 2) - 1) + 4) + 4) - 4) + 1| + 3)^2 - 3(2|(-2(1(-1(1cos(1\u03c0x - 2) - 1)^2 - 4(1cos(1\u03c0x - 2) - 1) + 4) + 4) - 4) + 1| + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(1(-4(4(2cos(2\u03c0(-3x^2 - 5x + 5)) + 3)^2 + 4(2cos(2\u03c0(-3x^2 - 5x + 5)) + 3) + 3) - 2) - 1))/(-2(1(-4(4(2cos(2\u03c0(-3x^2 - 5x + 5)) + 3)^2 + 4(2cos(2\u03c0(-3x^2 - 5x + 5)) + 3) + 3) - 2) - 1) - 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(-5(1|(-2(1cos(3\u03c0(-1|x| + 3) - 3) - 2)^2 + 3(1cos(3\u03c0(-1|x| + 3) - 3) - 2) + 2) - 2| - 3) - 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-4(1cos(3\u03c0(-5(2|(1x^2 + 3x - 2) + 2| + 1) - 4) + 2) + 1) + 2) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5((1((2(3(-2|(-2sin(3\u03c0x - 2)) - 2|)) + 2)/(-3(3(-2|(-2sin(3\u03c0x - 2)) - 2|)) + 4)) - 1)/(1((2(3(-2|(-2sin(3\u03c0x - 2)) - 2|)) + 2)/(-3(3(-2|(-2sin(3\u03c0x - 2)) - 2|)) + 4)) + 2))^2 + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(-5(-4((1(-3(1x^2 + 5x + 3) + 4))/(-2(-3(1x^2 + 5x + 3) + 4) + 1))^2 - 1((1(-3(1x^2 + 5x + 3) + 4))/(-2(-3(1x^2 + 5x + 3) + 4) + 1))) - 1)| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((-1(1|(-2|(-2(-1|x - 3| - 3) - 4) - 3|) + 2| - 2))/(2(1|(-2|(-2(-1|x - 3| - 3) - 4) - 3|) + 2| - 2) + 3))^2 - 1((-1(1|(-2|(-2(-1|x - 3| - 3) - 4) - 3|) + 2| - 2))/(2(1|(-2|(-2(-1|x - 3| - 3) - 4) - 3|) + 2| - 2) + 3)) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1sin(3\u03c0(-5(-3|((2(-5x^2 - 1x - 5) + 3)/(1(-5x^2 - 1x - 5) + 3)) + 1|) - 4) + 2) - 1) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((-3(1|(-1|(-1(3cos(2\u03c0x + 2) - 3)^2 - 3(3cos(2\u03c0x + 2) - 3) - 3) + 3| - 3) - 1| + 1) - 2)/(1(1|(-1|(-1(3cos(2\u03c0x + 2) - 3)^2 - 3(3cos(2\u03c0x + 2) - 3) - 3) + 3| - 3) - 1| + 1)))^2 - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(2|(-2(1(-3(-2cos(3\u03c0x - 2) + 1) + 2)^2 - 4(-3(-2cos(3\u03c0x - 2) + 1) + 2)) + 4) - 1| + 3) + 1)/(2(2|(-2(1(-3(-2cos(3\u03c0x - 2) + 1) + 2)^2 - 4(-3(-2cos(3\u03c0x - 2) + 1) + 2)) + 4) - 1| + 3) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(1((2((-1(-1|((-3x + 2)/(1x + 3)) + 3| + 3) + 3)/(-3(-1|((-3x + 2)/(1x + 3)) + 3| + 3) - 2)) + 2)/(-1((-1(-1|((-3x + 2)/(1x + 3)) + 3| + 3) + 3)/(-3(-1|((-3x + 2)/(1x + 3)) + 3| + 3) - 2)) + 2))^2 + 1((2((-1(-1|((-3x + 2)/(1x + 3)) + 3| + 3) + 3)/(-3(-1|((-3x + 2)/(1x + 3)) + 3| + 3) - 2)) + 2)/(-1((-1(-1|((-3x + 2)/(1x + 3)) + 3| + 3) + 3)/(-3(-1|((-3x + 2)/(1x + 3)) + 3| + 3) - 2)) + 2)) + 1) - 2| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-3cos(3\u03c0(4(-5(1(4x^2 + 1)^2 - 1(4x^2 + 1) - 3)^2 + 4(1(4x^2 + 1)^2 - 1(4x^2 + 1) - 3) - 1) - 1)) + 1) + 1)/(-3(-3cos(3\u03c0(4(-5(1(4x^2 + 1)^2 - 1(4x^2 + 1) - 3)^2 + 4(1(4x^2 + 1)^2 - 1(4x^2 + 1) - 3) - 1) - 1)) + 1) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-3(2cos(2\u03c0(1(3|((-2x + 1)/(3x - 2))| + 3)^2 + 1(3|((-2x + 1)/(3x - 2))| + 3) - 2) + 2) + 2) - 2) - 2| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(4(-1|(4(-4(-1sin(2\u03c0x - 1) + 3)^2 - 1(-1sin(2\u03c0x - 1) + 3) + 5) + 1) - 2| + 2) - 2) - 1)/(2(4(-1|(4(-4(-1sin(2\u03c0x - 1) + 3)^2 - 1(-1sin(2\u03c0x - 1) + 3) + 5) + 1) - 2| + 2) - 2) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(1|(3sin(1\u03c0(-3(2(-1x - 4) + 4)^2 + 4(2(-1x - 4) + 4) - 4) - 3)) - 3| + 1)^2 - 4(1|(3sin(1\u03c0(-3(2(-1x - 4) + 4)^2 + 4(2(-1x - 4) + 4) - 4) - 3)) - 3| + 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-2|(-3cos(2\u03c0(4(-2|(5x - 1) - 2|) + 4)) + 3) - 3| + 2) - 3| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1cos(3\u03c0(3(1|(3|(1|x - 2| + 2) + 1|) - 2| + 2)^2 + 3(1|(3|(1|x - 2| + 2) + 1|) - 2| + 2) + 2) - 2) + 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(-2sin(1\u03c0(-3(-5((-2(1x + 3) + 1)/(-1(1x + 3) - 3))^2 + 1((-2(1x + 3) + 1)/(-1(1x + 3) - 3)) + 2)^2 + 2(-5((-2(1x + 3) + 1)/(-1(1x + 3) - 3))^2 + 1((-2(1x + 3) + 1)/(-1(1x + 3) - 3)) + 2)) + 2) + 1)^2 + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-3(-1(3(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2)))^2 + 4(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2))) - 5)^2 - 3(3(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2)))^2 + 4(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2))) - 5) + 4) - 2)/(-1(-1(3(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2)))^2 + 4(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2))) - 5)^2 - 3(3(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2)))^2 + 4(2((3(4x + 1) - 1)/(2(4x + 1) + 2))^2 - 4((3(4x + 1) - 1)/(2(4x + 1) + 2))) - 5) + 4)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1((1(5((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2))^2 - 3((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2)) - 4) + 3)/(-2(5((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2))^2 - 3((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2)) - 4) + 1))^2 + 5((1(5((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2))^2 - 3((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2)) - 4) + 3)/(-2(5((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2))^2 - 3((2(-3sin(2\u03c0x - 1) + 1) - 3)/(1(-3sin(2\u03c0x - 1) + 1) - 2)) - 4) + 1)) - 1) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-3sin(1\u03c0((-3(2|((-2(3|x| - 3) - 3)/(-3(3|x| - 3) + 4)) - 1| + 1))/(-3(2|((-2(3|x| - 3) - 3)/(-3(3|x| - 3) + 4)) - 1| + 1) - 1)) - 1) + 2)^2 - 4(-3sin(1\u03c0((-3(2|((-2(3|x| - 3) - 3)/(-3(3|x| - 3) + 4)) - 1| + 1))/(-3(2|((-2(3|x| - 3) - 3)/(-3(3|x| - 3) + 4)) - 1| + 1) - 1)) - 1) + 2) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(3(3sin(3\u03c0(-1(4(3|x - 2| - 1)) + 3) + 1) - 2) + 4) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1((1(2sin(2\u03c0((1(-3((3x - 1)/(-3x - 1)) - 5) - 1)/(-3(-3((3x - 1)/(-3x - 1)) - 5))) + 1) + 1) - 3)/(2(2sin(2\u03c0((1(-3((3x - 1)/(-3x - 1)) - 5) - 1)/(-3(-3((3x - 1)/(-3x - 1)) - 5))) + 1) + 1))) - 3)/(-1((1(2sin(2\u03c0((1(-3((3x - 1)/(-3x - 1)) - 5) - 1)/(-3(-3((3x - 1)/(-3x - 1)) - 5))) + 1) + 1) - 3)/(2(2sin(2\u03c0((1(-3((3x - 1)/(-3x - 1)) - 5) - 1)/(-3(-3((3x - 1)/(-3x - 1)) - 5))) + 1) + 1)))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(1\u03c0((-1((-2(5((-1(-3x + 4) - 1)/(-1(-3x + 4)))^2 - 4((-1(-3x + 4) - 1)/(-1(-3x + 4))) + 3) - 1)/(-1(5((-1(-3x + 4) - 1)/(-1(-3x + 4)))^2 - 4((-1(-3x + 4) - 1)/(-1(-3x + 4))) + 3) - 3)) + 1)/(-1((-2(5((-1(-3x + 4) - 1)/(-1(-3x + 4)))^2 - 4((-1(-3x + 4) - 1)/(-1(-3x + 4))) + 3) - 1)/(-1(5((-1(-3x + 4) - 1)/(-1(-3x + 4)))^2 - 4((-1(-3x + 4) - 1)/(-1(-3x + 4))) + 3) - 3)) + 2)) + 2) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1|(4(2|(2(-2sin(3\u03c0x + 3) + 2) - 1) - 1| + 3) + 1) - 2| + 2) + 1)/(-2(1|(4(2|(2(-2sin(3\u03c0x + 3) + 2) - 1) - 1| + 3) + 1) - 2| + 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(1|(-2|(-1(3|(3sin(1\u03c0x + 2) - 2)| - 1) + 5) + 1| + 2) + 2|)^2 - 4(1|(-2|(-1(3|(3sin(1\u03c0x + 2) - 2)| - 1) + 5) + 1| + 2) + 2|) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|((-3((1(3|(-2cos(1\u03c0(-2x^2 - 3x - 1) - 1) + 3) + 1| + 2) - 2)/(2(3|(-2cos(1\u03c0(-2x^2 - 3x - 1) - 1) + 3) + 1| + 2) + 3)) + 2)/(-2((1(3|(-2cos(1\u03c0(-2x^2 - 3x - 1) - 1) + 3) + 1| + 2) - 2)/(2(3|(-2cos(1\u03c0(-2x^2 - 3x - 1) - 1) + 3) + 1| + 2) + 3)) - 3)) + 3| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-1|((-2(1(3(3sin(3\u03c0x - 3))^2 - 4)^2 + 2(3(3sin(3\u03c0x - 3))^2 - 4) + 5) - 1)/(3(1(3(3sin(3\u03c0x - 3))^2 - 4)^2 + 2(3(3sin(3\u03c0x - 3))^2 - 4) + 5) - 2))| + 2) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5((-2((2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) + 3)/(-2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) - 2)) - 3)/(-2((2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) + 3)/(-2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) - 2)) - 2))^2 + 2((-2((2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) + 3)/(-2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) - 2)) - 3)/(-2((2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) + 3)/(-2(-3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1)))^2 + 3((-1(1cos(2\u03c0x + 1) - 1) - 1)/(2(1cos(2\u03c0x + 1) - 1))) + 5) - 2)) - 2)) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(3cos(3\u03c0(2((3(2((-3x - 2)/(2x)) + 1) + 2)/(2(2((-3x - 2)/(2x)) + 1) + 1))^2 - 1((3(2((-3x - 2)/(2x)) + 1) + 2)/(2(2((-3x - 2)/(2x)) + 1) + 1)) + 4) - 1) + 2) + 2)/(2(3cos(3\u03c0(2((3(2((-3x - 2)/(2x)) + 1) + 2)/(2(2((-3x - 2)/(2x)) + 1) + 1))^2 - 1((3(2((-3x - 2)/(2x)) + 1) + 2)/(2(2((-3x - 2)/(2x)) + 1) + 1)) + 4) - 1) + 2)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2sin(1\u03c0(2(-2|(5((-1(-5x - 2) + 2)/(-2(-5x - 2))) + 3) + 3| - 1)^2 - 3(-2|(5((-1(-5x - 2) + 2)/(-2(-5x - 2))) + 3) + 3| - 1) + 2) - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5((2(-2(-2cos(3\u03c0((-1((-1x + 2)/(3x)) + 2)/(2((-1x + 2)/(3x)) - 1))) + 3)^2 - 3(-2cos(3\u03c0((-1((-1x + 2)/(3x)) + 2)/(2((-1x + 2)/(3x)) - 1))) + 3) + 1))/(3(-2(-2cos(3\u03c0((-1((-1x + 2)/(3x)) + 2)/(2((-1x + 2)/(3x)) - 1))) + 3)^2 - 3(-2cos(3\u03c0((-1((-1x + 2)/(3x)) + 2)/(2((-1x + 2)/(3x)) - 1))) + 3) + 1) + 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(5(-3sin(3\u03c0((2((-2(1x - 3))/(3(1x - 3) - 2)) + 2)/(-2((-2(1x - 3))/(3(1x - 3) - 2)) + 1)) + 2) + 3) + 3) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(1\u03c0((-2(3(-4((-1(-3|x - 3| + 1))/(-1(-3|x - 3| + 1) - 3)) - 4)^2 - 3(-4((-1(-3|x - 3| + 1))/(-1(-3|x - 3| + 1) - 3)) - 4) - 1) - 2)/(-1(3(-4((-1(-3|x - 3| + 1))/(-1(-3|x - 3| + 1) - 3)) - 4)^2 - 3(-4((-1(-3|x - 3| + 1))/(-1(-3|x - 3| + 1) - 3)) - 4) - 1) + 3)) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1((-3(-2(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5)^2 + 5(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5) + 1) + 3)/(-1(-2(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5)^2 + 5(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5) + 1) + 2)))/(-2((-3(-2(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5)^2 + 5(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5) + 1) + 3)/(-1(-2(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5)^2 + 5(4(-1|((-2x)/(-1x - 3))| + 2)^2 - 2(-1|((-2x)/(-1x - 3))| + 2) - 5) + 1) + 2)) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(3cos(1\u03c0(2((3(3|(1x^2 - 5x + 4) - 2| - 1) - 1)/(-2(3|(1x^2 - 5x + 4) - 2| - 1) - 3))^2 - 2((3(3|(1x^2 - 5x + 4) - 2| - 1) - 1)/(-2(3|(1x^2 - 5x + 4) - 2| - 1) - 3))) + 3) - 1) - 3| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1sin(2\u03c0(-3|(-3(-1(-1((-1x - 2)/(2x - 1))^2 - 1((-1x - 2)/(2x - 1)) + 5)^2 - 2(-1((-1x - 2)/(2x - 1))^2 - 1((-1x - 2)/(2x - 1)) + 5) + 4)^2 + 3(-1(-1((-1x - 2)/(2x - 1))^2 - 1((-1x - 2)/(2x - 1)) + 5)^2 - 2(-1((-1x - 2)/(2x - 1))^2 - 1((-1x - 2)/(2x - 1)) + 5) + 4) - 1) - 3| - 1) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(1(-4((1(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) + 3)/(2(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) - 1))^2 - 2)^2 + 1(-4((1(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) + 3)/(2(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) - 1))^2 - 2) - 2) + 3)/(1(1(-4((1(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) + 3)/(2(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) - 1))^2 - 2)^2 + 1(-4((1(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) + 3)/(2(-1cos(3\u03c0((-2x + 2)/(2x - 1)) + 1) + 3) - 1))^2 - 2) - 2) - 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(1\u03c0(4(1|((-3(2(-4x^2 + 4)^2 + 5(-4x^2 + 4) - 1) - 2)/(-3(2(-4x^2 + 4)^2 + 5(-4x^2 + 4) - 1) + 2)) + 2| - 3)^2 + 2(1|((-3(2(-4x^2 + 4)^2 + 5(-4x^2 + 4) - 1) - 2)/(-3(2(-4x^2 + 4)^2 + 5(-4x^2 + 4) - 1) + 2)) + 2| - 3) - 5) - 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(-2(2cos(3\u03c0(-3|(1((-1x + 1)/(-3x - 2))^2 + 1((-1x + 1)/(-3x - 2)) - 3) + 2| + 1) - 3)) - 3)^2 - 1(-2(2cos(3\u03c0(-3|(1((-1x + 1)/(-3x - 2))^2 + 1((-1x + 1)/(-3x - 2)) - 3) + 2| + 1) - 3)) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(3(2|((-1((-1(-5x - 5) - 3)/(2(-5x - 5) - 1)) + 2)/(2((-1(-5x - 5) - 3)/(2(-5x - 5) - 1)))) + 3| - 3)^2 + 5(2|((-1((-1(-5x - 5) - 3)/(2(-5x - 5) - 1)) + 2)/(2((-1(-5x - 5) - 3)/(2(-5x - 5) - 1)))) + 3| - 3) - 2)| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2sin(1\u03c0(2(-1(-5(-2|((-3x + 1)/(2x)) + 3| + 2) + 5) - 3)) + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(1sin(1\u03c0(-2(1|(-4(-2x - 3)^2 - 3(-2x - 3) + 4) - 3| + 3) - 2)) + 2)^2 - 1(1sin(1\u03c0(-2(1|(-4(-2x - 3)^2 - 3(-2x - 3) + 4) - 3| + 3) - 2)) + 2) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(1|(3(-1(-2sin(2\u03c0(3x^2 - 2x + 1) - 1) + 2) + 3) + 5) - 2|) + 2)/(3(1|(3(-1(-2sin(2\u03c0(3x^2 - 2x + 1) - 1) + 2) + 3) + 5) - 2|) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(5(2sin(3\u03c0(-1(-3((-2x - 2)/(-3x + 2)) - 2)^2 + 1(-3((-2x - 2)/(-3x + 2)) - 2) + 2) - 3) + 3) - 3) + 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2((2(-1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2)^2 - 1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2) - 2) - 2)/(1(-1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2)^2 - 1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2) - 2))) + 2)/(2((2(-1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2)^2 - 1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2) - 2) - 2)/(1(-1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2)^2 - 1(-5(1cos(1\u03c0(3x^2 + 5x + 4) - 3))^2 + 3(1cos(1\u03c0(3x^2 + 5x + 4) - 3)) + 2) - 2))) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(-1(3(1(2(-1|x| + 2))^2 + 1(2(-1|x| + 2)) - 4) - 1) - 2)^2 + 1(-1(3(1(2(-1|x| + 2))^2 + 1(2(-1|x| + 2)) - 4) - 1) - 2) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-3(-5(-3sin(3\u03c0(5(-3((3x - 1)/(-3x - 3))^2 + 4((3x - 1)/(-3x - 3)) - 2) - 3) - 1) + 3) - 4) + 1)/(-1(-5(-3sin(3\u03c0(5(-3((3x - 1)/(-3x - 3))^2 + 4((3x - 1)/(-3x - 3)) - 2) - 3) - 1) + 3) - 4) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(2sin(1\u03c0(-2(3(1(-2|x - 1|) + 4) + 3) - 4) - 2) - 3)^2 - 3(2sin(1\u03c0(-2(3(1(-2|x - 1|) + 4) + 3) - 4) - 2) - 3) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(3sin(2\u03c0(-1|(2((1((-2x + 3)/(-3x - 2)) + 2)/(-1((-2x + 3)/(-3x - 2)) + 2))^2 - 4((1((-2x + 3)/(-3x - 2)) + 2)/(-1((-2x + 3)/(-3x - 2)) + 2)) + 3) - 2| + 1) + 1) - 1) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3sin(3\u03c0(-4((-1(-1|(-1(-2x^2 - 1x + 2)^2 + 4(-2x^2 - 1x + 2) - 4) + 1|) - 1)/(-1(-1|(-1(-2x^2 - 1x + 2)^2 + 4(-2x^2 - 1x + 2) - 4) + 1|) - 3)) + 5) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(-3(2cos(3\u03c0(1(-5((3x - 2)/(1x - 3)) + 5)^2 - 4) - 1) + 2) + 1) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3((2((2(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) - 1)/(3(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) + 2)) + 1)/(1((2(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) - 1)/(3(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) + 2)) - 2)))/(-2((2((2(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) - 1)/(3(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) + 2)) + 1)/(1((2(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) - 1)/(3(2|(3cos(3\u03c0(3x + 5) - 3) + 2) - 2|) + 2)) - 2)) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|((-2(-1cos(2\u03c0(-3(-1(1|x - 2| + 3) - 2)^2 + 2(-1(1|x - 2| + 3) - 2) + 4) - 1)) - 2)/(-3(-1cos(2\u03c0(-3(-1(1|x - 2| + 3) - 2)^2 + 2(-1(1|x - 2| + 3) - 2) + 4) - 1)) + 1)) + 1| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2((3(2sin(2\u03c0((-1((-3(-2|x + 3| - 2) - 2)/(2(-2|x + 3| - 2) - 1)) + 2)/(-1((-3(-2|x + 3| - 2) - 2)/(2(-2|x + 3| - 2) - 1)) - 2)) + 2) + 2) - 3)/(-1(2sin(2\u03c0((-1((-3(-2|x + 3| - 2) - 2)/(2(-2|x + 3| - 2) - 1)) + 2)/(-1((-3(-2|x + 3| - 2) - 2)/(2(-2|x + 3| - 2) - 1)) - 2)) + 2) + 2) - 3)) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((1(-2|(1sin(1\u03c0(-4(2|x - 3| - 3) + 4) - 3) - 1) + 2| + 3) - 1)/(2(-2|(1sin(1\u03c0(-4(2|x - 3| - 3) + 4) - 3) - 1) + 2| + 3)))^2 + 4((1(-2|(1sin(1\u03c0(-4(2|x - 3| - 3) + 4) - 3) - 1) + 2| + 3) - 1)/(2(-2|(1sin(1\u03c0(-4(2|x - 3| - 3) + 4) - 3) - 1) + 2| + 3))) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3((2(3(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1)^2 + 4(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1) - 2) - 3)/(-2(3(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1)^2 + 4(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1) - 2) - 1)) - 2)/(3((2(3(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1)^2 + 4(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1) - 2) - 3)/(-2(3(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1)^2 + 4(4(1(1cos(3\u03c0x + 3) - 2) - 4) + 1) - 2) - 1)) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(3|(1cos(3\u03c0(-2|(-2|(-2|x - 2| - 2) + 2|) - 3| + 2) + 3) - 3) - 2|) + 2)/(2(3|(1cos(3\u03c0(-2|(-2|(-2|x - 2| - 2) + 2|) - 3| + 2) + 3) - 3) - 2|)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|((1(-3|(-1|(3cos(2\u03c0((-3x - 3)/(-1x + 2)) - 3) - 2) + 2| + 1) + 3| - 2) - 3)/(3(-3|(-1|(3cos(2\u03c0((-3x - 3)/(-1x + 2)) - 3) - 2) + 2| + 1) + 3| - 2) - 1)) - 1| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-1cos(1\u03c0(-2(-4(-2|(2|x - 1| + 3) + 3| - 2)^2 + 1(-2|(2|x - 1| + 3) + 3| - 2) + 1) + 1) - 1) - 1)| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-1sin(2\u03c0((3((-2(1((-1x + 3)/(2x)) + 3) + 2)/(-1(1((-1x + 3)/(2x)) + 3) - 2)) - 3)/(-3((-2(1((-1x + 3)/(2x)) + 3) + 2)/(-1(1((-1x + 3)/(2x)) + 3) - 2)))) - 2) - 2))/(2(-1sin(2\u03c0((3((-2(1((-1x + 3)/(2x)) + 3) + 2)/(-1(1((-1x + 3)/(2x)) + 3) - 2)) - 3)/(-3((-2(1((-1x + 3)/(2x)) + 3) + 2)/(-1(1((-1x + 3)/(2x)) + 3) - 2)))) - 2) - 2) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|((-2(-1(-3(4(-3|x - 2| + 2) + 4)^2 + 5)^2 - 3(-3(4(-3|x - 2| + 2) + 4)^2 + 5) + 2))/(3(-1(-3(4(-3|x - 2| + 2) + 4)^2 + 5)^2 - 3(-3(4(-3|x - 2| + 2) + 4)^2 + 5) + 2) - 1)) - 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1(-2cos(3\u03c0(-2((3(-2x^2 + 1x + 3) - 2)/(1(-2x^2 + 1x + 3)))^2 - 2) + 1) - 3) - 5) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((1(-2|((1(-4(1x^2 + 3x)^2 - 3(1x^2 + 3x) + 2) - 2)/(1(-4(1x^2 + 3x)^2 - 3(1x^2 + 3x) + 2) + 1)) - 1|) + 3)/(2(-2|((1(-4(1x^2 + 3x)^2 - 3(1x^2 + 3x) + 2) - 2)/(1(-4(1x^2 + 3x)^2 - 3(1x^2 + 3x) + 2) + 1)) - 1|) + 2))| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-5((-1(3cos(2\u03c0(3(-1x - 2)^2 - 2(-1x - 2) + 1) + 2) - 3) - 3)/(-2(3cos(2\u03c0(3(-1x - 2)^2 - 2(-1x - 2) + 1) + 2) - 3) + 3)) + 5)^2 - 4(-5((-1(3cos(2\u03c0(3(-1x - 2)^2 - 2(-1x - 2) + 1) + 2) - 3) - 3)/(-2(3cos(2\u03c0(3(-1x - 2)^2 - 2(-1x - 2) + 1) + 2) - 3) + 3)) + 5) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2((-2(5(-2sin(2\u03c0(-2(-4x^2 + 2x)^2 + 1(-4x^2 + 2x) - 4) - 3)) - 4) + 2)/(2(5(-2sin(2\u03c0(-2(-4x^2 + 2x)^2 + 1(-4x^2 + 2x) - 4) - 3)) - 4) - 1)))/(3((-2(5(-2sin(2\u03c0(-2(-4x^2 + 2x)^2 + 1(-4x^2 + 2x) - 4) - 3)) - 4) + 2)/(2(5(-2sin(2\u03c0(-2(-4x^2 + 2x)^2 + 1(-4x^2 + 2x) - 4) - 3)) - 4) - 1)) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-5(-1sin(1\u03c0(-2|(1|(-1|x| + 1) - 1| - 3) - 1| + 2) - 2) + 1)^2 + 3(-1sin(1\u03c0(-2|(1|(-1|x| + 1) - 1| - 3) - 1| + 2) - 2) + 1) - 5) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1((-3(-3sin(2\u03c0(-5(-1((2x + 3)/(1x + 3)) - 2)^2 + 2(-1((2x + 3)/(1x + 3)) - 2) + 2)) - 3))/(-2(-3sin(2\u03c0(-5(-1((2x + 3)/(1x + 3)) - 2)^2 + 2(-1((2x + 3)/(1x + 3)) - 2) + 2)) - 3) + 1)) + 1)/(-1((-3(-3sin(2\u03c0(-5(-1((2x + 3)/(1x + 3)) - 2)^2 + 2(-1((2x + 3)/(1x + 3)) - 2) + 2)) - 3))/(-2(-3sin(2\u03c0(-5(-1((2x + 3)/(1x + 3)) - 2)^2 + 2(-1((2x + 3)/(1x + 3)) - 2) + 2)) - 3) + 1)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2((-1(5(-2|(2cos(1\u03c0x + 1) + 1) - 1|)^2 + 2(-2|(2cos(1\u03c0x + 1) + 1) - 1|) - 1) + 3)/(2(5(-2|(2cos(1\u03c0x + 1) + 1) - 1|)^2 + 2(-2|(2cos(1\u03c0x + 1) + 1) - 1|) - 1))) - 4)^2 - 1(-2((-1(5(-2|(2cos(1\u03c0x + 1) + 1) - 1|)^2 + 2(-2|(2cos(1\u03c0x + 1) + 1) - 1|) - 1) + 3)/(2(5(-2|(2cos(1\u03c0x + 1) + 1) - 1|)^2 + 2(-2|(2cos(1\u03c0x + 1) + 1) - 1|) - 1))) - 4) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((-1((-1(1|((2(-2|x + 1| - 3) - 1)/(-1(-2|x + 1| - 3) - 3)) + 3| - 1) - 2)/(2(1|((2(-2|x + 1| - 3) - 1)/(-1(-2|x + 1| - 3) - 3)) + 3| - 1) + 1)) - 3)/(1((-1(1|((2(-2|x + 1| - 3) - 1)/(-1(-2|x + 1| - 3) - 3)) + 3| - 1) - 2)/(2(1|((2(-2|x + 1| - 3) - 1)/(-1(-2|x + 1| - 3) - 3)) + 3| - 1) + 1)))) + 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2sin(1\u03c0(-4(-5(1((-1x - 3)/(2x)))^2 - 3(1((-1x - 3)/(2x))) - 1) - 3) + 1) - 1)^2 + 4(2sin(1\u03c0(-4(-5(1((-1x - 3)/(2x)))^2 - 3(1((-1x - 3)/(2x))) - 1) - 3) + 1) - 1) - 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-2((3((1(4(2sin(1\u03c0x - 1) - 1)^2 - 1(2sin(1\u03c0x - 1) - 1) - 3))/(2(4(2sin(1\u03c0x - 1) - 1)^2 - 1(2sin(1\u03c0x - 1) - 1) - 3) - 1)) + 1)/(-2((1(4(2sin(1\u03c0x - 1) - 1)^2 - 1(2sin(1\u03c0x - 1) - 1) - 3))/(2(4(2sin(1\u03c0x - 1) - 1)^2 - 1(2sin(1\u03c0x - 1) - 1) - 3) - 1)) + 3)) - 1) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(2(1(3|(-1|(-2sin(3\u03c0x + 1) + 1) + 3| + 3)| - 2)^2 + 5(3|(-1|(-2sin(3\u03c0x + 1) + 1) + 3| + 3)| - 2) - 5) + 3) - 3)/(-3(2(1(3|(-1|(-2sin(3\u03c0x + 1) + 1) + 3| + 3)| - 2)^2 + 5(3|(-1|(-2sin(3\u03c0x + 1) + 1) + 3| + 3)| - 2) - 5) + 3) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-1cos(2\u03c0((-3((2(3(-2|x - 1| + 2) - 2) - 1)/(-1(3(-2|x - 1| + 2) - 2) + 2)) + 1)/(1((2(3(-2|x - 1| + 2) - 2) - 1)/(-1(3(-2|x - 1| + 2) - 2) + 2)) + 2))) + 2) - 3)/(2(-1cos(2\u03c0((-3((2(3(-2|x - 1| + 2) - 2) - 1)/(-1(3(-2|x - 1| + 2) - 2) + 2)) + 1)/(1((2(3(-2|x - 1| + 2) - 2) - 1)/(-1(3(-2|x - 1| + 2) - 2) + 2)) + 2))) + 2) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2sin(3\u03c0(1(-2(3|((-2((2x - 1)/(3x + 3)) - 3)/(-3((2x - 1)/(3x + 3)) - 3)) - 3| + 3)^2 + 3(3|((-2((2x - 1)/(3x + 3)) - 3)/(-3((2x - 1)/(3x + 3)) - 3)) - 3| + 3) + 4) + 5) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-3(5(-2sin(3\u03c0((1(-5((-2x)/(-2x - 1))^2) + 2)/(-2(-5((-2x)/(-2x - 1))^2) - 1))))^2 - 4(-2sin(3\u03c0((1(-5((-2x)/(-2x - 1))^2) + 2)/(-2(-5((-2x)/(-2x - 1))^2) - 1)))) + 5) - 3)/(-1(5(-2sin(3\u03c0((1(-5((-2x)/(-2x - 1))^2) + 2)/(-2(-5((-2x)/(-2x - 1))^2) - 1))))^2 - 4(-2sin(3\u03c0((1(-5((-2x)/(-2x - 1))^2) + 2)/(-2(-5((-2x)/(-2x - 1))^2) - 1)))) + 5) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1(2(2cos(2\u03c0(-2|(-3x - 5) - 2|) - 3) - 3) - 5) - 1))/(-1(-1(2(2cos(2\u03c0(-2|(-3x - 5) - 2|) - 3) - 3) - 5) - 1) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(1\u03c0(-3(-2|(-1(-1(-3|x| - 2) - 1)^2 + 2(-1(-3|x| - 2) - 1) - 3) - 2| - 2) + 4) - 2) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-3|(-1(-1(1(1x^2 - 3)^2 + 3(1x^2 - 3) - 2)^2 - 4(1(1x^2 - 3)^2 + 3(1x^2 - 3) - 2)) - 5) - 2| - 1) + 2)/(2(-3|(-1(-1(1(1x^2 - 3)^2 + 3(1x^2 - 3) - 2)^2 - 4(1(1x^2 - 3)^2 + 3(1x^2 - 3) - 2)) - 5) - 2| - 1) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(-1|(1e^(-1(-1|(1(4x + 4)^2 + 1(4x + 4)) - 1| + 2)) - 2)| - 1) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-1|(-3(-1(-1|(-2x^2 + 1x + 3) - 1| + 1)^2 - 1) - 4) + 1|) - 2)/(-1(-1|(-3(-1(-1|(-2x^2 + 1x + 3) - 1| + 1)^2 - 1) - 4) + 1|) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(2cos(1\u03c0(-4(5((3(2x^2 - 1x - 4) - 2)/(-1(2x^2 - 1x - 4) + 2))^2 - 4((3(2x^2 - 1x - 4) - 2)/(-1(2x^2 - 1x - 4) + 2))) - 2) - 1) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(-3|(-5(2|(-3|((-1x - 2)/(-2x + 3)) - 1| + 3) - 2| - 2) + 1)| + 1)^2 - 2(-3|(-5(2|(-3|((-1x - 2)/(-2x + 3)) - 1| + 3) - 2| - 2) + 1)| + 1) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(2(1|((2(-2|(-1|x + 1| + 3) + 1| + 2) + 3)/(2(-2|(-1|x + 1| + 3) + 1| + 2))) + 1| + 1) - 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3((-1((2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 3)/(-2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 1)) - 3)/(-2((2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 3)/(-2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 1)) + 3)) + 2)/(-2((-1((2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 3)/(-2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 1)) - 3)/(-2((2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 3)/(-2(3(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3)^2 - 4(-3cos(1\u03c0(1|x - 2| - 2) + 3) - 3) + 3) - 1)) + 3)) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((-2((2(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 3)/(1(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 1)) - 3)/(2((2(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 3)/(1(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 1)) + 1))^2 - 2((-2((2(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 3)/(1(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 1)) - 3)/(2((2(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 3)/(1(-5(3(3cos(1\u03c0x - 3) - 3) + 1) - 5) + 1)) + 1)) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(3|(-3cos(3\u03c0(5((2((1x)/(1x - 3)) - 1)/(-1((1x)/(1x - 3)) - 2)) - 4) - 2) - 2)| + 1)^2 - 4(3|(-3cos(3\u03c0(5((2((1x)/(1x - 3)) - 1)/(-1((1x)/(1x - 3)) - 2)) - 4) - 2) - 2)| + 1) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(3|(-1(-1sin(2\u03c0(-1(2|x - 1| - 2)^2 - 2(2|x - 1| - 2) - 1) + 1) + 2)^2 + 4)| - 1)^2 + 3(3|(-1(-1sin(2\u03c0(-1(2|x - 1| - 2)^2 - 2(2|x - 1| - 2) - 1) + 1) + 2)^2 + 4)| - 1) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-1(4(2sin(2\u03c0((-2(4x - 4) + 3)/(1(4x - 4) + 1)) - 1) + 1) + 4) + 4)^2 + 2(-1(4(2sin(2\u03c0((-2(4x - 4) + 3)/(1(4x - 4) + 1)) - 1) + 1) + 4) + 4) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-2|(-2|(1cos(3\u03c0((-1(-1x^2 - 1x + 3) - 3)/(-1(-1x^2 - 1x + 3))) - 3) + 1) + 3| - 3) - 2| - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((-2(1(2sin(1\u03c0((3(-1x^2 + 5x + 5) - 2)/(2(-1x^2 + 5x + 5) + 3)) - 1) - 3) - 1) - 1)/(-2(1(2sin(1\u03c0((3(-1x^2 + 5x + 5) - 2)/(2(-1x^2 + 5x + 5) + 3)) - 1) - 3) - 1) + 1))^2 - 2((-2(1(2sin(1\u03c0((3(-1x^2 + 5x + 5) - 2)/(2(-1x^2 + 5x + 5) + 3)) - 1) - 3) - 1) - 1)/(-2(1(2sin(1\u03c0((3(-1x^2 + 5x + 5) - 2)/(2(-1x^2 + 5x + 5) + 3)) - 1) - 3) - 1) + 1)) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((1(1(-1cos(1\u03c0(3|((-1x + 1)/(-1x - 1)) - 2| + 1) + 3) + 1) - 3) + 1)/(-2(1(-1cos(1\u03c0(3|((-1x + 1)/(-1x - 1)) - 2| + 1) + 3) + 1) - 3) + 3))^2 + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-4(1(-1cos(2\u03c0(3|(-1x^2 + 1x + 5)| - 3) - 2) - 2)^2 + 5(-1cos(2\u03c0(3|(-1x^2 + 1x + 5)| - 3) - 2) - 2) + 3) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(5(2(4(1((-3x - 2)/(-1x + 2))^2 - 1((-3x - 2)/(-1x + 2)) - 3)^2 + 5(1((-3x - 2)/(-1x + 2))^2 - 1((-3x - 2)/(-1x + 2)) - 3) - 1) + 2) - 1) - 2| + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(1|(3|(-3sin(3\u03c0(-1(-2|x + 3| + 1)^2 + 3(-2|x + 3| + 1) - 1) - 2) + 2) + 3| - 2) + 1| - 3) + 2| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(2cos(1\u03c0(3(1(-3|(-1x) + 1|)) + 3) + 3) - 2) - 1| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(1(-5((1((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) + 1)/(-2((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) - 3)) + 5)^2 + 3(-5((1((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) + 1)/(-2((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) - 3)) + 5)) - 3)/(-1(1(-5((1((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) + 1)/(-2((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) - 3)) + 5)^2 + 3(-5((1((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) + 1)/(-2((2(-3sin(3\u03c0x) + 2))/(-2(-3sin(3\u03c0x) + 2) - 1)) - 3)) + 5)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(2sin(2\u03c0((-3((-1(-4(1x^2 - 2x - 2) + 3))/(-1(-4(1x^2 - 2x - 2) + 3) + 2)))/(-3((-1(-4(1x^2 - 2x - 2) + 3))/(-1(-4(1x^2 - 2x - 2) + 3) + 2)) - 3)) + 3) - 3) + 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(4(-1|(-3(1|(2cos(3\u03c0x + 1) + 1) + 1| + 3)^2 + 1) - 2| - 2) - 5) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(1sin(3\u03c0(2(3|((1(-1x^2 + 4x + 2) - 2)/(2(-1x^2 + 4x + 2) + 3)) - 1|) - 2)) - 3) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-2cos(3\u03c0(4(-4(3(2x^2 - 1x - 2) - 4) + 4))) + 3) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(4(1|(2(-3|(1cos(2\u03c0x - 3) - 3) - 2| + 3) - 2)| - 2) + 1) + 1| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(2cos(2\u03c0((-2(1|((1(2|x - 1| + 2) - 2)/(2(2|x - 1| + 2) - 1)) + 1|))/(-3(1|((1(2|x - 1| + 2) - 2)/(2(2|x - 1| + 2) - 1)) + 1|) + 4)) + 1) + 1) + 1| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(-1((1(-1|((-1(2sin(2\u03c0x - 2) + 3) - 2)/(-3(2sin(2\u03c0x - 2) + 3) - 1)) + 2| + 2))/(-3(-1|((-1(2sin(2\u03c0x - 2) + 3) - 2)/(-3(2sin(2\u03c0x - 2) + 3) - 1)) + 2| + 2) - 2))^2 + 1((1(-1|((-1(2sin(2\u03c0x - 2) + 3) - 2)/(-3(2sin(2\u03c0x - 2) + 3) - 1)) + 2| + 2))/(-3(-1|((-1(2sin(2\u03c0x - 2) + 3) - 2)/(-3(2sin(2\u03c0x - 2) + 3) - 1)) + 2| + 2) - 2)) - 2)^2 + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|((3(3(-2(-5(2cos(1\u03c0x + 1) - 3)^2 - 1(2cos(1\u03c0x + 1) - 3) + 1)) - 5) + 3)/(2(3(-2(-5(2cos(1\u03c0x + 1) - 3)^2 - 1(2cos(1\u03c0x + 1) - 3) + 1)) - 5) + 3)) - 1| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(3|((-3(-1cos(3\u03c0(1|(-1|x - 1| + 2) + 3| - 3) - 3) - 1) - 2)/(2(-1cos(3\u03c0(1|(-1|x - 1| + 2) + 3| - 3) - 3) - 1) + 3)) + 1| - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(1(2cos(3\u03c0(-1(-1|((2x + 1)/(3x - 2)) - 3| + 2)^2 + 1(-1|((2x + 1)/(3x - 2)) - 3| + 2) + 1)))^2 + 2(2cos(3\u03c0(-1(-1|((2x + 1)/(3x - 2)) - 3| + 2)^2 + 1(-1|((2x + 1)/(3x - 2)) - 3| + 2) + 1)))) + 1| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-2|((1(1sin(3\u03c0(-1(2|x - 3| + 1)^2 + 4(2|x - 3| + 1) + 1) - 1) - 2) + 3)/(-1(1sin(3\u03c0(-1(2|x - 3| + 1)^2 + 4(2|x - 3| + 1) + 1) - 1) - 2) + 2)) - 1| - 3)^2 + 5(-2|((1(1sin(3\u03c0(-1(2|x - 3| + 1)^2 + 4(2|x - 3| + 1) + 1) - 1) - 2) + 3)/(-1(1sin(3\u03c0(-1(2|x - 3| + 1)^2 + 4(2|x - 3| + 1) + 1) - 1) - 2) + 2)) - 1| - 3) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(5((3(2cos(1\u03c0((-2((1x - 3)/(2x + 3)) + 3)/(3((1x - 3)/(2x + 3)) - 1)) - 1) + 3) - 3)/(-1(2cos(1\u03c0((-2((1x - 3)/(2x + 3)) + 3)/(3((1x - 3)/(2x + 3)) - 1)) - 1) + 3) - 2)) - 5)^2 + 4(5((3(2cos(1\u03c0((-2((1x - 3)/(2x + 3)) + 3)/(3((1x - 3)/(2x + 3)) - 1)) - 1) + 3) - 3)/(-1(2cos(1\u03c0((-2((1x - 3)/(2x + 3)) + 3)/(3((1x - 3)/(2x + 3)) - 1)) - 1) + 3) - 2)) - 5) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5((-1(-2cos(1\u03c0(-4((2(2|x - 3|) - 2)/(1(2|x - 3|) + 3))^2 - 2((2(2|x - 3|) - 2)/(1(2|x - 3|) + 3)) + 2) + 3) + 3) - 2)/(-2(-2cos(1\u03c0(-4((2(2|x - 3|) - 2)/(1(2|x - 3|) + 3))^2 - 2((2(2|x - 3|) - 2)/(1(2|x - 3|) + 3)) + 2) + 3) + 3) - 3)) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(1\u03c0(2|(2((-2(1(-3x^2 + 3x)^2 + 5(-3x^2 + 3x) + 5) + 1)/(3(1(-3x^2 + 3x)^2 + 5(-3x^2 + 3x) + 5) - 1)) - 5) - 2| + 2) - 2) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((3(1(-3(-3(1sin(3\u03c0x + 3) + 2) + 4) - 2) - 4))/(-3(1(-3(-3(1sin(3\u03c0x + 3) + 2) + 4) - 2) - 4) + 1)) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((-2(-1((1(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) + 3)/(-2(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) - 3))^2 + 4((1(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) + 3)/(-2(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) - 3))) + 2)/(-2(-1((1(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) + 3)/(-2(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) - 3))^2 + 4((1(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) + 3)/(-2(2cos(3\u03c0(-1x^2 + 4x - 4)) - 2) - 3))) + 3)) + 2| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3((-2((-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 3)/(-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 2)) + 2)/(1((-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 3)/(-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 2)) + 1)))/(1((-2((-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 3)/(-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 2)) + 2)/(1((-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 3)/(-2(1cos(2\u03c0(-1|(-3x - 2) - 3| + 2) - 2) + 2) - 2)) + 1)) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-1((-2(3|(5(-1cos(2\u03c0x + 1))^2 + 5(-1cos(2\u03c0x + 1)) - 2) - 1| + 3) + 3)/(3(3|(5(-1cos(2\u03c0x + 1))^2 + 5(-1cos(2\u03c0x + 1)) - 2) - 1| + 3) + 2)) - 2)^2 + 5(-1((-2(3|(5(-1cos(2\u03c0x + 1))^2 + 5(-1cos(2\u03c0x + 1)) - 2) - 1| + 3) + 3)/(3(3|(5(-1cos(2\u03c0x + 1))^2 + 5(-1cos(2\u03c0x + 1)) - 2) - 1| + 3) + 2)) - 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1(2(-2|(4(2|x + 2| - 2)^2 + 5(2|x + 2| - 2)) - 2| + 3)^2 - 2) + 2) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-1(3(-3cos(1\u03c0(3|(-2|x + 3| - 1) - 3| - 3) - 1) - 3) + 3) - 3) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-3|(-3cos(1\u03c0((1(-3((1x - 3)/(1x + 2)) - 1))/(-1(-3((1x - 3)/(1x + 2)) - 1) - 2)) + 1) + 2) + 3| + 3) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(-3(-5(3cos(1\u03c0(-3((-2x + 3)/(-3x - 1))^2 - 1((-2x + 3)/(-3x - 1)) + 3) + 1) + 1) + 1) - 3)| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(1sin(2\u03c0(-1|(-4(2|(1x + 1) - 3|)^2 + 4(2|(1x + 1) - 3|) - 1) - 3| + 1) - 3) + 3) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(4(-3cos(2\u03c0(2|((-3(3x - 1) - 3)/(1(3x - 1) - 2)) - 1| - 1)) - 1)^2 + 2(-3cos(2\u03c0(2|((-3(3x - 1) - 3)/(1(3x - 1) - 2)) - 1| - 1)) - 1)) + 1| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-4(2|(-2cos(1\u03c0(-3|(-3|x + 2| + 3) + 1| + 2)) - 2)| - 3) + 5), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-3(1(2sin(2\u03c0(1|(-3x^2 - 4x + 3) + 1|)) + 1)^2 - 4(2sin(2\u03c0(1|(-3x^2 - 4x + 3) + 1|)) + 1) - 2) + 4) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2((-2(1(2(-1(-3cos(2\u03c0x - 1) - 3) - 2) + 2) + 4))/(-1(1(2(-1(-3cos(2\u03c0x - 1) - 3) - 2) + 2) + 4) - 1)) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1|(1(3sin(1\u03c0(-3|(4x - 4) - 1| - 3) + 3) - 2)^2 + 2(3sin(1\u03c0(-3|(4x - 4) - 1| - 3) + 3) - 2) - 4) - 1| - 1) - 3| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(4(1((3(2(3cos(3\u03c0x + 3) - 1) - 3) - 1)/(2(2(3cos(3\u03c0x + 3) - 1) - 3) + 2))^2 + 5((3(2(3cos(3\u03c0x + 3) - 1) - 3) - 1)/(2(2(3cos(3\u03c0x + 3) - 1) - 3) + 2)))^2 - 3(1((3(2(3cos(3\u03c0x + 3) - 1) - 3) - 1)/(2(2(3cos(3\u03c0x + 3) - 1) - 3) + 2))^2 + 5((3(2(3cos(3\u03c0x + 3) - 1) - 3) - 1)/(2(2(3cos(3\u03c0x + 3) - 1) - 3) + 2))) - 5) - 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(-5(-1|(-2|(-1|(4x^2 + 4x - 2) - 3| + 1)| - 1) - 2| + 3)^2 - 2(-1|(-2|(-1|(4x^2 + 4x - 2) - 3| + 1)| - 1) - 2| + 3) + 5) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5(-1((-3(2(-3cos(2\u03c0(-5x^2 + 5x + 1) + 2) - 2) - 5) - 2)/(2(2(-3cos(2\u03c0(-5x^2 + 5x + 1) + 2) - 2) - 5) + 2)) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-1(-2|(-2cos(1\u03c0(5(-1x^2 + 3x + 3)^2 - 4(-1x^2 + 3x + 3) - 4) + 3) - 3) + 3| + 3)^2 - 3(-2|(-2cos(1\u03c0(5(-1x^2 + 3x + 3)^2 - 4(-1x^2 + 3x + 3) - 4) + 3) - 3) + 3| + 3) - 4)| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3((1(-2sin(1\u03c0(1(1((-3x + 2)/(-1x + 2)) - 5) - 4) + 1) + 1) + 3)/(-3(-2sin(1\u03c0(1(1((-3x + 2)/(-1x + 2)) - 5) - 4) + 1) + 1) + 1))^2 + 2((1(-2sin(1\u03c0(1(1((-3x + 2)/(-1x + 2)) - 5) - 4) + 1) + 1) + 3)/(-3(-2sin(1\u03c0(1(1((-3x + 2)/(-1x + 2)) - 5) - 4) + 1) + 1) + 1)) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2((-2(-2(-2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3)^2 + 2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3) + 3)^2 - 5(-2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3)^2 + 2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3) + 3) + 1) + 1)/(2(-2(-2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3)^2 + 2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3) + 3)^2 - 5(-2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3)^2 + 2(1sin(3\u03c0(5x^2 + 3x - 1) + 3) + 3) + 3) + 1))) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1|(-3|(4(2cos(2\u03c0(4x - 4) - 1) + 2) + 2) + 3|) + 2| + 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(-2sin(2\u03c0(5((-2(-2(1|x| + 2) + 5) - 2)/(1(-2(1|x| + 2) + 5) - 2)) + 5)) - 1) - 1)/(-3(-2sin(2\u03c0(5((-2(-2(1|x| + 2) + 5) - 2)/(1(-2(1|x| + 2) + 5) - 2)) + 5)) - 1)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(3(5(3|((1(-1x^2 - 2x + 5) + 3)/(1(-1x^2 - 2x + 5) + 1)) - 1| - 2) + 2) - 5) + 3| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(1(-1|(1|(-1sin(1\u03c0(2x^2 - 2x + 1) - 3) + 1) + 2| + 1) + 3|)^2 + 2(-1|(1|(-1sin(1\u03c0(2x^2 - 2x + 1) - 3) + 1) + 2| + 1) + 3|) + 3) + 2| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(-2(-3sin(2\u03c0(3(-1((-1x + 1)/(1x - 3))^2 - 1((-1x + 1)/(1x - 3)))^2 - 3(-1((-1x + 1)/(1x - 3))^2 - 1((-1x + 1)/(1x - 3))) - 3)) + 3) - 3) + 3)/(-2(-2(-3sin(2\u03c0(3(-1((-1x + 1)/(1x - 3))^2 - 1((-1x + 1)/(1x - 3)))^2 - 3(-1((-1x + 1)/(1x - 3))^2 - 1((-1x + 1)/(1x - 3))) - 3)) + 3) - 3) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(1(-3(2sin(3\u03c0(-3|((3x + 1)/(2x - 1)) - 3| + 2) - 3) + 2)^2)^2 + 5(-3(2sin(3\u03c0(-3|((3x + 1)/(2x - 1)) - 3| + 2) - 3) + 2)^2) - 4)^2 + 5(1(-3(2sin(3\u03c0(-3|((3x + 1)/(2x - 1)) - 3| + 2) - 3) + 2)^2)^2 + 5(-3(2sin(3\u03c0(-3|((3x + 1)/(2x - 1)) - 3| + 2) - 3) + 2)^2) - 4) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(1((-1((1(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) + 1)/(3(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) - 2)))/(-2((1(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) + 1)/(3(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) - 2)) + 1)) + 2)^2 - 5(1((-1((1(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) + 1)/(3(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) - 2)))/(-2((1(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) + 1)/(3(3|(1sin(1\u03c0x - 2) - 2) - 3| - 1) - 2)) + 1)) + 2) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-2(-1cos(3\u03c0(-3((2(-1x + 5) - 1)/(3(-1x + 5) + 2))^2 + 3((2(-1x + 5) - 1)/(3(-1x + 5) + 2)) + 2) - 2)) + 3)^2 - 4(-2(-1cos(3\u03c0(-3((2(-1x + 5) - 1)/(3(-1x + 5) + 2))^2 + 3((2(-1x + 5) - 1)/(3(-1x + 5) + 2)) + 2) - 2)) + 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(-2|(-2|(1(1(-1x + 5)^2 - 3(-1x + 5)) - 5)| + 3) - 2| + 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2((1(1(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3)^2 - 4(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3) + 2) + 3)/(-2(1(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3)^2 - 4(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3) + 2) - 3)) - 2)/(3((1(1(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3)^2 - 4(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3) + 2) + 3)/(-2(1(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3)^2 - 4(3sin(3\u03c0(-4(3|x + 3| + 2)^2 - 4(3|x + 3| + 2) + 4)) + 3) + 2) - 3)) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(2cos(2\u03c0(-1(2|(1(-2x + 1) + 5)| - 1)^2 + 4(2|(1(-2x + 1) + 5)| - 1) - 4) - 3) + 1) - 2)/(1(2cos(2\u03c0(-1(2|(1(-2x + 1) + 5)| - 1)^2 + 4(2|(1(-2x + 1) + 5)| - 1) - 4) - 3) + 1) + 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(1(-3sin(3\u03c0(2|(-1|(-4x + 3) + 2| - 2) + 1| + 3) - 2) + 3) - 2)^2 - 3(1(-3sin(3\u03c0(2|(-1|(-4x + 3) + 2| - 2) + 1| + 3) - 2) + 3) - 2) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-1sin(2\u03c0(2|(-3|(4(-3x^2 + 1x + 1) + 3)| + 1) + 3| + 1) + 2) - 3) + 3| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4((-2(-1((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))^2 - 5((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))) - 2)/(2(-1((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))^2 - 5((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))) + 1))^2 + 1((-2(-1((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))^2 - 5((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))) - 2)/(2(-1((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))^2 - 5((3(5(2cos(1\u03c0x + 1) - 2) + 3) - 3)/(3(5(2cos(1\u03c0x + 1) - 2) + 3) + 3))) + 1)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((-2(1|(-4(1|(-3cos(3\u03c0x) + 1)| + 2)^2 - 2(1|(-3cos(3\u03c0x) + 1)| + 2) - 5)| + 3) + 2)/(3(1|(-4(1|(-3cos(3\u03c0x) + 1)| + 2)^2 - 2(1|(-3cos(3\u03c0x) + 1)| + 2) - 5)| + 3) + 2))^2 - 2((-2(1|(-4(1|(-3cos(3\u03c0x) + 1)| + 2)^2 - 2(1|(-3cos(3\u03c0x) + 1)| + 2) - 5)| + 3) + 2)/(3(1|(-4(1|(-3cos(3\u03c0x) + 1)| + 2)^2 - 2(1|(-3cos(3\u03c0x) + 1)| + 2) - 5)| + 3) + 2)) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|((-3(-2sin(2\u03c0(1|(2|((-1x - 1)/(1x - 3)) + 2| + 3) + 1| - 3) - 1) + 1) + 3)/(-3(-2sin(2\u03c0(1|(2|((-1x - 1)/(1x - 3)) + 2| + 3) + 1| - 3) - 1) + 1))) + 1| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3((-2(-2(-2(2|(2cos(2\u03c0x + 3) + 2) - 1|) + 1) + 3) - 3)/(3(-2(-2(2|(2cos(2\u03c0x + 3) + 2) - 1|) + 1) + 3) + 1)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(1|(1cos(1\u03c0(-3(-1|(-3x^2 - 2x + 5) + 1| + 2) - 4) + 3) - 1)| - 3) - 1)/(-1(1|(1cos(1\u03c0(-3(-1|(-3x^2 - 2x + 5) + 1| + 2) - 4) + 3) - 1)| - 3) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|((3(1|(1((3(-2sin(3\u03c0x + 1) + 1) + 2)/(-1(-2sin(3\u03c0x + 1) + 1) - 2)) + 4) - 1| - 1) + 1)/(3(1|(1((3(-2sin(3\u03c0x + 1) + 1) + 2)/(-1(-2sin(3\u03c0x + 1) + 1) - 2)) + 4) - 1| - 1) - 2)) + 2| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(-1(2sin(2\u03c0(-2|((1(-4x + 2))/(-2(-4x + 2) - 3)) - 1| + 3) + 1) - 2)^2 - 5(2sin(2\u03c0(-2|((1(-4x + 2))/(-2(-4x + 2) - 3)) - 1| + 3) + 1) - 2) - 4)^2 + 1(-1(2sin(2\u03c0(-2|((1(-4x + 2))/(-2(-4x + 2) - 3)) - 1| + 3) + 1) - 2)^2 - 5(2sin(2\u03c0(-2|((1(-4x + 2))/(-2(-4x + 2) - 3)) - 1| + 3) + 1) - 2) - 4) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(1|(-1((-2(-2sin(3\u03c0(4x + 3) + 2) + 3) + 3)/(-2(-2sin(3\u03c0(4x + 3) + 2) + 3) - 1))^2 - 2((-2(-2sin(3\u03c0(4x + 3) + 2) + 3) + 3)/(-2(-2sin(3\u03c0(4x + 3) + 2) + 3) - 1)) + 3) - 1| + 3) - 1)/(-1(1|(-1((-2(-2sin(3\u03c0(4x + 3) + 2) + 3) + 3)/(-2(-2sin(3\u03c0(4x + 3) + 2) + 3) - 1))^2 - 2((-2(-2sin(3\u03c0(4x + 3) + 2) + 3) + 3)/(-2(-2sin(3\u03c0(4x + 3) + 2) + 3) - 1)) + 3) - 1| + 3) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(-4((2(-3sin(1\u03c0(-4(5x^2 + 4x + 2) + 4)) - 3) - 2)/(2(-3sin(1\u03c0(-4(5x^2 + 4x + 2) + 4)) - 3) - 1))^2 - 2((2(-3sin(1\u03c0(-4(5x^2 + 4x + 2) + 4)) - 3) - 2)/(2(-3sin(1\u03c0(-4(5x^2 + 4x + 2) + 4)) - 3) - 1)) - 3) - 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1sin(1\u03c0(-2(1(1|(1x) + 1| + 1)^2 - 1(1|(1x) + 1| + 1) - 3) - 5) + 2) + 3)^2 - 5(-1sin(1\u03c0(-2(1(1|(1x) + 1| + 1)^2 - 1(1|(1x) + 1| + 1) - 3) - 5) + 2) + 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(1cos(2\u03c0(1(2|(1|((1x)/(-2x - 1)) - 3| + 1) + 1|) + 1)) - 3) + 3| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-3|((-2((-2(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1))/(3(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1) + 2)) - 3)/(-2((-2(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1))/(3(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1) + 2)))) - 1|) + 1)/(3(-3|((-2((-2(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1))/(3(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1) + 2)) - 3)/(-2((-2(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1))/(3(-3sin(3\u03c0((1x)/(3x - 2)) + 3) - 1) + 2)))) - 1|) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(5(-4(-1(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3)^2 + 4(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3) + 1) + 5)^2 - 4(-4(-1(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3)^2 + 4(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3) + 1) + 5) - 3))/(2(5(-4(-1(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3)^2 + 4(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3) + 1) + 5)^2 - 4(-4(-1(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3)^2 + 4(-2cos(2\u03c0((3x + 3)/(-2x + 3)) + 1) - 3) + 1) + 5) - 3) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(-1|(-1(1|(-1|(4x + 1) - 2| - 1)| - 3)^2 + 2(1|(-1|(4x + 1) - 2| - 1)| - 3) + 3) + 2| - 3) - 2)/(1(-1|(-1(1|(-1|(4x + 1) - 2| - 1)| - 3)^2 + 2(1|(-1|(4x + 1) - 2| - 1)| - 3) + 3) + 2| - 3)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|((-1(3cos(3\u03c0(-3|(3((-2x - 3)/(-1x - 1)) + 3)| - 1) - 3) - 2) - 1)/(3(3cos(3\u03c0(-3|(3((-2x - 3)/(-1x - 1)) + 3)| - 1) - 3) - 2) - 1)) + 1| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(2|(-1|(1(2|(4x - 1) - 3| - 3) + 4) + 1| + 3) + 3| - 3)^2 + 4(2|(-1|(1(2|(4x - 1) - 3| - 3) + 4) + 1| + 3) + 3| - 3) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(1cos(2\u03c0(2(-5((-2((1x + 3)/(1x + 2)) - 3)/(3((1x + 3)/(1x + 2)) + 1)) - 4) + 4)) + 2) - 2)/(3(1cos(2\u03c0(2(-5((-2((1x + 3)/(1x + 2)) - 3)/(3((1x + 3)/(1x + 2)) + 1)) - 4) + 4)) + 2) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(1(-1(1|((1(1x + 2) + 1)/(-3(1x + 2) + 4)) + 2| - 1)^2 - 1(1|((1(1x + 2) + 1)/(-3(1x + 2) + 4)) + 2| - 1) + 5)^2 - 1(-1(1|((1(1x + 2) + 1)/(-3(1x + 2) + 4)) + 2| - 1)^2 - 1(1|((1(1x + 2) + 1)/(-3(1x + 2) + 4)) + 2| - 1) + 5) + 1) - 3| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(2|(-3(1|(1|(4x^2 + 2x - 3) + 2| - 2) - 3| - 3)^2 - 4(1|(1|(4x^2 + 2x - 3) + 2| - 2) - 3| - 3) + 5) - 1|)| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(-2|(-1(-2((-3(-1|x| + 3) - 1)/(-3(-1|x| + 3) + 2)) + 3)^2 + 5) - 2| - 3) - 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-1((3(-3e^(-1((3(-2|x| + 2) - 1)/(-1(-2|x| + 2)))) + 1) - 3)/(3(-3e^(-1((3(-2|x| + 2) - 1)/(-1(-2|x| + 2)))) + 1) + 1))^2 - 4((3(-3e^(-1((3(-2|x| + 2) - 1)/(-1(-2|x| + 2)))) + 1) - 3)/(3(-3e^(-1((3(-2|x| + 2) - 1)/(-1(-2|x| + 2)))) + 1) + 1)) + 2) + 1| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(3(-3|(-1(1|(-2cos(3\u03c0x - 2) + 1) + 1| + 2) - 5) + 3|) + 5) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|((-2((-1((1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) - 2)/(-1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) + 3)) + 2)/(-3((1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) - 2)/(-1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) + 3)) + 2)) - 3)/(-3((-1((1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) - 2)/(-1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) + 3)) + 2)/(-3((1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) - 2)/(-1(-2|(-3sin(3\u03c0x + 2) - 2) - 2| - 3) + 3)) + 2)) + 2)) + 2| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((2(-4(-3|(1|(-1sin(1\u03c0x - 1) + 2) + 1| - 2) + 1|)^2 - 5(-3|(1|(-1sin(1\u03c0x - 1) + 2) + 1| - 2) + 1|) - 5) + 1)/(1(-4(-3|(1|(-1sin(1\u03c0x - 1) + 2) + 1| - 2) + 1|)^2 - 5(-3|(1|(-1sin(1\u03c0x - 1) + 2) + 1| - 2) + 1|) - 5) - 3)) + 3| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2((-1(-2(-3(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5)^2 - 2(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5) + 5)^2 + 4(-3(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5)^2 - 2(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5) + 5) - 1) + 1)/(2(-2(-3(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5)^2 - 2(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5) + 5)^2 + 4(-3(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5)^2 - 2(3(-3sin(3\u03c0x - 2))^2 - 1(-3sin(3\u03c0x - 2)) + 5) + 5) - 1) - 1)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(-2sin(1\u03c0(3|(2(1|(2x^2 + 4) - 3| + 1)) - 1| + 3) - 2) + 1) - 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(1\u03c0(-2|((2(-2|(1(-5x^2 - 3x + 2) + 3) + 3| - 1) - 3)/(2(-2|(1(-5x^2 - 3x + 2) + 3) + 3| - 1) + 1)) + 3|) + 3) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(2sin(1\u03c0(-1(-4(-3((-1x + 2)/(-2x + 3)) + 3)^2 - 4(-3((-1x + 2)/(-2x + 3)) + 3) + 1) - 5) + 2) + 2)^2 - 3(2sin(1\u03c0(-1(-4(-3((-1x + 2)/(-2x + 3)) + 3)^2 - 4(-3((-1x + 2)/(-2x + 3)) + 3) + 1) - 5) + 2) + 2) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1((3(-4(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1)^2 + 1(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1) + 5) + 2)/(2(-4(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1)^2 + 1(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1) + 5) - 3)))/(3((3(-4(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1)^2 + 1(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1) + 5) + 2)/(2(-4(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1)^2 + 1(2|(-2cos(1\u03c0(4x^2 + 3x - 2) + 2) - 3) + 2| + 1) + 5) - 3)) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(1(-1|(-3cos(1\u03c0(-1|(-2x^2 - 3x - 3)| + 3) - 1) - 2) + 2| + 3) + 5)^2 + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(-3|(2sin(2\u03c0(-3(4((1x + 2)/(1x - 3)) + 1)^2 + 5(4((1x + 2)/(1x - 3)) + 1) - 2) + 3) + 2) - 2| + 1)^2 + 5(-3|(2sin(2\u03c0(-3(4((1x + 2)/(1x - 3)) + 1)^2 + 5(4((1x + 2)/(1x - 3)) + 1) - 2) + 3) + 2) - 2| + 1) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((1(-1|(-1((3(3cos(2\u03c0x - 2) - 3) - 2)/(-3(3cos(2\u03c0x - 2) - 3)))^2 - 3((3(3cos(2\u03c0x - 2) - 3) - 2)/(-3(3cos(2\u03c0x - 2) - 3))) - 2) - 3| + 2) - 3)/(-1(-1|(-1((3(3cos(2\u03c0x - 2) - 3) - 2)/(-3(3cos(2\u03c0x - 2) - 3)))^2 - 3((3(3cos(2\u03c0x - 2) - 3) - 2)/(-3(3cos(2\u03c0x - 2) - 3))) - 2) - 3| + 2) - 2)) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(4(-3((-3(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)/(-2(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)) + 1)^2 + 2(-3((-3(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)/(-2(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)) + 1) - 4) + 1)/(3(4(-3((-3(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)/(-2(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)) + 1)^2 + 2(-3((-3(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)/(-2(2(-3cos(3\u03c0x - 1) - 3)^2 + 1(-3cos(3\u03c0x - 1) - 3) - 4) + 1)) + 1) - 4) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((-1((1(-3cos(3\u03c0(-3(-2x^2 - 3x - 3) + 3) - 3) + 3) - 1)/(-1(-3cos(3\u03c0(-3(-2x^2 - 3x - 3) + 3) - 3) + 3) - 2)) + 1)/(2((1(-3cos(3\u03c0(-3(-2x^2 - 3x - 3) + 3) - 3) + 3) - 1)/(-1(-3cos(3\u03c0(-3(-2x^2 - 3x - 3) + 3) - 3) + 3) - 2)) + 3)) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(5((1(2cos(1\u03c0(3|((-1x - 1)/(1x - 3)) + 2| + 2) - 1) - 3) - 3)/(-3(2cos(1\u03c0(3|((-1x - 1)/(1x - 3)) + 2| + 2) - 1) - 3) + 1)))^2 - 1(5((1(2cos(1\u03c0(3|((-1x - 1)/(1x - 3)) + 2| + 2) - 1) - 3) - 3)/(-3(2cos(1\u03c0(3|((-1x - 1)/(1x - 3)) + 2| + 2) - 1) - 3) + 1))) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(4(1(-1(3|(-1|x - 2| - 1) + 3| + 3)^2 + 4(3|(-1|x - 2| - 1) + 3| + 3) - 4) + 4)^2 + 4(1(-1(3|(-1|x - 2| - 1) + 3| + 3)^2 + 4(3|(-1|x - 2| - 1) + 3| + 3) - 4) + 4) - 2) - 1| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(1\u03c0(1(-2((-1(-2|((2x - 2)/(-3x + 4))| - 1) + 3)/(1(-2|((2x - 2)/(-3x + 4))| - 1)))^2 - 1((-1(-2|((2x - 2)/(-3x + 4))| - 1) + 3)/(1(-2|((2x - 2)/(-3x + 4))| - 1))) + 5)^2) - 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2((-1((-2(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) + 2)/(-3(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) - 3)) - 2)/(2((-2(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) + 2)/(-3(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) - 3)))) + 1)/(2((-1((-2(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) + 2)/(-3(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) - 3)) - 2)/(2((-2(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) + 2)/(-3(1cos(1\u03c0(-2(-5x - 2) - 1) - 1)) - 3)))) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-5(-1(-1sin(1\u03c0((1(-3x^2 - 2x + 4) + 3)/(-1(-3x^2 - 2x + 4) + 3)) - 3) - 2) - 3) - 3) + 1| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(3((-2((1(-3sin(1\u03c0((3x - 2)/(-3x - 2)) - 3) - 3))/(1(-3sin(1\u03c0((3x - 2)/(-3x - 2)) - 3) - 3) - 3)) + 2)/(-1((1(-3sin(1\u03c0((3x - 2)/(-3x - 2)) - 3) - 3))/(1(-3sin(1\u03c0((3x - 2)/(-3x - 2)) - 3) - 3) - 3)) + 2)) + 1) - 2| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(1|(1sin(3\u03c0(1(-2|(4x + 2) - 3| + 3) + 4) + 1) - 1) - 2| + 1) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-3(-3sin(1\u03c0(-2|((-2(1x + 1) + 2)/(2(1x + 1) + 2)) - 2| - 3) - 1) - 2) + 3) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(2|(-3cos(2\u03c0(-4(2(-1x^2 + 1x + 2) + 1) + 5) + 3) + 2) + 1| + 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(2\u03c0(2|(4(-3(-1(-3|x + 2| - 1)^2 - 1(-3|x + 2| - 1) - 1) + 4) - 5) + 1| + 2) + 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|((3((-2(1|(1(1cos(2\u03c0x + 2) + 3)^2 + 4(1cos(2\u03c0x + 2) + 3) - 2)| - 1) - 3)/(3(1|(1(1cos(2\u03c0x + 2) + 3)^2 + 4(1cos(2\u03c0x + 2) + 3) - 2)| - 1) + 3)) - 2)/(1((-2(1|(1(1cos(2\u03c0x + 2) + 3)^2 + 4(1cos(2\u03c0x + 2) + 3) - 2)| - 1) - 3)/(3(1|(1(1cos(2\u03c0x + 2) + 3)^2 + 4(1cos(2\u03c0x + 2) + 3) - 2)| - 1) + 3)) - 2)) + 3| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((-3(-1(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1)^2 + 4(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1) - 2) - 1)/(-2(-1(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1)^2 + 4(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1) - 2)))^2 + 3((-3(-1(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1)^2 + 4(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1) - 2) - 1)/(-2(-1(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1)^2 + 4(1cos(2\u03c0((1(-4x) - 1)/(2(-4x) + 3)) - 2) - 1) - 2))) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5((3(2|(5(1cos(2\u03c0(-1x - 4) - 1) + 3)^2 - 2(1cos(2\u03c0(-1x - 4) - 1) + 3)) + 2|) + 3)/(3(2|(5(1cos(2\u03c0(-1x - 4) - 1) + 3)^2 - 2(1cos(2\u03c0(-1x - 4) - 1) + 3)) + 2|) + 1))^2 - 4((3(2|(5(1cos(2\u03c0(-1x - 4) - 1) + 3)^2 - 2(1cos(2\u03c0(-1x - 4) - 1) + 3)) + 2|) + 3)/(3(2|(5(1cos(2\u03c0(-1x - 4) - 1) + 3)^2 - 2(1cos(2\u03c0(-1x - 4) - 1) + 3)) + 2|) + 1)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-2(2sin(2\u03c0((3((1(5x) - 1)/(3(5x) + 3)))/(-3((1(5x) - 1)/(3(5x) + 3)) - 1))) + 2)^2 - 4(2sin(2\u03c0((3((1(5x) - 1)/(3(5x) + 3)))/(-3((1(5x) - 1)/(3(5x) + 3)) - 1))) + 2) + 5) - 3| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((3(2(-1|(1cos(3\u03c0(1|x + 2| - 2) + 3) + 3) - 1| + 1)^2 - 1(-1|(1cos(3\u03c0(1|x + 2| - 2) + 3) + 3) - 1| + 1)) - 1)/(-3(2(-1|(1cos(3\u03c0(1|x + 2| - 2) + 3) + 3) - 1| + 1)^2 - 1(-1|(1cos(3\u03c0(1|x + 2| - 2) + 3) + 3) - 1| + 1)) + 4)) + 2| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(2(1|(2|(1|(-2x^2 + 3x + 2) - 1| - 2) + 2| - 2) - 3|) - 5) + 1| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1|(-1|(-3(-2(-5x^2 + 4x)^2 + 1(-5x^2 + 4x) + 1)^2 - 4(-2(-5x^2 + 4x)^2 + 1(-5x^2 + 4x) + 1) + 4) + 2|) - 1| - 3)^2 + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((2(-1|(-3(3cos(2\u03c0(-2|x - 3| - 2) - 1) + 3) - 3) + 2| - 3))/(-3(-1|(-3(3cos(2\u03c0(-2|x - 3| - 2) - 1) + 3) - 3) + 2| - 3) - 2))^2 - 2((2(-1|(-3(3cos(2\u03c0(-2|x - 3| - 2) - 1) + 3) - 3) + 2| - 3))/(-3(-1|(-3(3cos(2\u03c0(-2|x - 3| - 2) - 1) + 3) - 3) + 2| - 3) - 2)) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-3|(-5(-1((2(-1|x + 1| + 3) - 1)/(1(-1|x + 1| + 3) + 1)) + 1) - 3) + 3| + 1) + 3| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1(1|(-3|(-3|(1sin(2\u03c0x - 1)) - 1| - 2) + 2| + 1)| - 1)^2 + 1(1|(-3|(-3|(1sin(2\u03c0x - 1)) - 1| - 2) + 2| + 1)| - 1) - 3) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(2|((-1(-3sin(1\u03c0(-2|((-1x - 3)/(-2x + 3)) + 3| - 3) + 1) + 1) + 3)/(-1(-3sin(1\u03c0(-2|((-1x - 3)/(-2x + 3)) + 3| - 3) + 1) + 1) + 2))|) - 1| - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(2\u03c0(-2|(4(-1|(-1|((2x + 1)/(1x + 2)) - 2| - 1) - 1| - 2) - 1) + 3| - 2) + 3) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(-4(-3sin(3\u03c0(-2|((-2(-3x + 5) + 1)/(1(-3x + 5) - 3))| - 2) - 1) + 1) + 2) - 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-3|(-2|(2|(1|(-1|x + 2| - 1)| - 3) - 1| - 2) + 1| + 3) - 2| + 2)^2 + 2(-3|(-2|(2|(1|(-1|x + 2| - 1)| - 3) - 1| - 2) + 1| + 3) - 2| + 2) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(1|(-2(1(-3|(2x - 2) - 3| + 2)^2 - 2(-3|(2x - 2) - 3| + 2) - 1)^2 + 5) - 3| - 1) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-2(-2sin(1\u03c0((3(-3((-3x + 3)/(-2x))^2 - 4((-3x + 3)/(-2x)) + 5) + 1)/(-2(-3((-3x + 3)/(-2x))^2 - 4((-3x + 3)/(-2x)) + 5) - 3)) - 3) + 2)^2 - 4(-2sin(1\u03c0((3(-3((-3x + 3)/(-2x))^2 - 4((-3x + 3)/(-2x)) + 5) + 1)/(-2(-3((-3x + 3)/(-2x))^2 - 4((-3x + 3)/(-2x)) + 5) - 3)) - 3) + 2) + 4) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(3\u03c0((-2(-4((1(-4(-4x - 2)^2 + 2(-4x - 2) - 4) + 3)/(2(-4(-4x - 2)^2 + 2(-4x - 2) - 4) - 3))^2 + 5((1(-4(-4x - 2)^2 + 2(-4x - 2) - 4) + 3)/(2(-4(-4x - 2)^2 + 2(-4x - 2) - 4) - 3)) + 1) + 3)/(-1(-4((1(-4(-4x - 2)^2 + 2(-4x - 2) - 4) + 3)/(2(-4(-4x - 2)^2 + 2(-4x - 2) - 4) - 3))^2 + 5((1(-4(-4x - 2)^2 + 2(-4x - 2) - 4) + 3)/(2(-4(-4x - 2)^2 + 2(-4x - 2) - 4) - 3)) + 1) + 2)) + 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1(2cos(3\u03c0((-1(-3|(1|x - 3| - 3) + 2| + 3) + 1)/(-3(-3|(1|x - 3| - 3) + 2| + 3) + 2)) + 1) - 1)^2 + 3(2cos(3\u03c0((-1(-3|(1|x - 3| - 3) + 2| + 3) + 1)/(-3(-3|(1|x - 3| - 3) + 2| + 3) + 2)) + 1) - 1) - 5)^2 - 3(1(2cos(3\u03c0((-1(-3|(1|x - 3| - 3) + 2| + 3) + 1)/(-3(-3|(1|x - 3| - 3) + 2| + 3) + 2)) + 1) - 1)^2 + 3(2cos(3\u03c0((-1(-3|(1|x - 3| - 3) + 2| + 3) + 1)/(-3(-3|(1|x - 3| - 3) + 2| + 3) + 2)) + 1) - 1) - 5) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(3\u03c0(3(-1|(1(2(-1x - 3)^2 + 3(-1x - 3) + 4) - 4)| - 2)) + 3) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((-3(-2cos(2\u03c0(-1|((1(1|x + 1| + 3))/(1(1|x + 1| + 3) - 3)) + 1| - 1) + 3) + 2) + 3)/(2(-2cos(2\u03c0(-1|((1(1|x + 1| + 3))/(1(1|x + 1| + 3) - 3)) + 1| - 1) + 3) + 2) + 3)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(1\u03c0(2|(3|(3(2((3x + 3)/(2x - 1)) - 3) + 3) + 1| - 3)| - 1)) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1sin(1\u03c0(1(-2|((2((2x + 1)/(2x)) - 2)/(-1((2x + 1)/(2x)) + 2)) + 2| + 1)^2 + 3(-2|((2((2x + 1)/(2x)) - 2)/(-1((2x + 1)/(2x)) + 2)) + 2| + 1) + 2)) + 2)^2 - 1(1sin(1\u03c0(1(-2|((2((2x + 1)/(2x)) - 2)/(-1((2x + 1)/(2x)) + 2)) + 2| + 1)^2 + 3(-2|((2((2x + 1)/(2x)) - 2)/(-1((2x + 1)/(2x)) + 2)) + 2| + 1) + 2)) + 2) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(2|((3((-3(-2cos(3\u03c0((-2x - 3)/(2x - 1)) - 2)) - 3)/(3(-2cos(3\u03c0((-2x - 3)/(2x - 1)) - 2)) - 2)))/(3((-3(-2cos(3\u03c0((-2x - 3)/(2x - 1)) - 2)) - 3)/(3(-2cos(3\u03c0((-2x - 3)/(2x - 1)) - 2)) - 2)) - 1))|) + 3|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1(-3(1sin(1\u03c0(1(-1x + 3) + 4) - 3) - 1) - 4) + 4) - 2)/(1(1(-3(1sin(1\u03c0(1(-1x + 3) + 4) - 3) - 1) - 4) + 4) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((2((-1(3sin(1\u03c0((-1(2|x + 2| - 1))/(1(2|x + 2| - 1) - 2)) + 3) + 3) + 1)/(-1(3sin(1\u03c0((-1(2|x + 2| - 1))/(1(2|x + 2| - 1) - 2)) + 3) + 3) + 3)) - 2)/(1((-1(3sin(1\u03c0((-1(2|x + 2| - 1))/(1(2|x + 2| - 1) - 2)) + 3) + 3) + 1)/(-1(3sin(1\u03c0((-1(2|x + 2| - 1))/(1(2|x + 2| - 1) - 2)) + 3) + 3) + 3)) - 3)) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(1|(5(4(1(-1sin(1\u03c0x - 3) - 3) - 3) - 1) - 4) + 2|) + 1)/(3(1|(5(4(1(-1sin(1\u03c0x - 3) - 3) - 3) - 1) - 4) + 2|) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(3cos(1\u03c0(-2(5(-4((-2x + 2)/(3x - 2)) + 4)^2 - 4(-4((-2x + 2)/(3x - 2)) + 4) - 1) + 5) + 1) + 3)^2 + 2(3cos(1\u03c0(-2(5(-4((-2x + 2)/(3x - 2)) + 4)^2 - 4(-4((-2x + 2)/(3x - 2)) + 4) - 1) + 5) + 1) + 3) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(3((3(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2)/(-1(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2))^2 - 4((3(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2)/(-1(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2)) + 4)^2 - 5(3((3(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2)/(-1(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2))^2 - 4((3(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2)/(-1(-1((1(3cos(1\u03c0x - 2) - 3) + 1)/(-2(3cos(1\u03c0x - 2) - 3) + 3)) + 5) + 2)) + 4) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(1|(-3|(-3cos(2\u03c0(3((3x - 2)/(1x + 1))^2 + 1((3x - 2)/(1x + 1))) + 3) + 1) + 2| - 1)| - 1) - 1| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2|(4(-3|(3|(-2x - 2)| - 3) - 2| + 3)^2 - 1(-3|(3|(-2x - 2)| - 3) - 2| + 3) - 1) + 3|) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(2|(3(-2cos(2\u03c0(4(1|x + 1|) - 5) + 3) - 1)) + 2|) + 3)/(-2(2|(3(-2cos(2\u03c0(4(1|x + 1|) - 5) + 3) - 1)) + 2|)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(1|(-2|(5(-2sin(2\u03c0(-1x + 5)) + 3) + 5) + 1| - 2) + 1| - 2) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(1\u03c0(-3(1(2((3(-4x + 3))/(2(-4x + 3) + 2)) - 5)^2 + 1(2((3(-4x + 3))/(2(-4x + 3) + 2)) - 5) - 2) - 5)) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(-2|(-1((-3(3cos(3\u03c0(5x + 4) - 2)) + 1)/(-2(3cos(3\u03c0(5x + 4) - 2)))) - 2)| + 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-5(-1sin(3\u03c0((2(2|((2x + 1)/(3x - 2)) - 2| - 1) - 2)/(2(2|((2x + 1)/(3x - 2)) - 2| - 1) - 3)) + 1) + 1) - 4) - 3| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((-3(-3|((3(-1(1cos(1\u03c0x + 2) + 3) - 1) + 1)/(-1(-1(1cos(1\u03c0x + 2) + 3) - 1) + 3)) - 2| + 3))/(-2(-3|((3(-1(1cos(1\u03c0x + 2) + 3) - 1) + 1)/(-1(-1(1cos(1\u03c0x + 2) + 3) - 1) + 3)) - 2| + 3) + 1))^2 + 5((-3(-3|((3(-1(1cos(1\u03c0x + 2) + 3) - 1) + 1)/(-1(-1(1cos(1\u03c0x + 2) + 3) - 1) + 3)) - 2| + 3))/(-2(-3|((3(-1(1cos(1\u03c0x + 2) + 3) - 1) + 1)/(-1(-1(1cos(1\u03c0x + 2) + 3) - 1) + 3)) - 2| + 3) + 1)) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(1\u03c0(2(1|((-1(-2(-1x - 1)^2 + 4) + 2)/(-1(-2(-1x - 1)^2 + 4) - 1)) - 2| + 3) - 5) - 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-5((2(3(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2)^2 - 1(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2) + 4) + 3)/(3(3(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2)^2 - 1(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2) + 4) + 2)) - 2))/(2(-5((2(3(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2)^2 - 1(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2) + 4) + 3)/(3(3(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2)^2 - 1(1cos(1\u03c0((1x - 3)/(-2x - 2)) - 3) - 2) + 4) + 2)) - 2) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(3|((3(3cos(1\u03c0(1((-3x - 1)/(-1x - 2))^2 - 1((-3x - 1)/(-1x - 2)) + 3) + 2) + 1))/(3(3cos(1\u03c0(1((-3x - 1)/(-1x - 2))^2 - 1((-3x - 1)/(-1x - 2)) + 3) + 2) + 1) - 1)) + 1| + 2) - 2)/(3(3|((3(3cos(1\u03c0(1((-3x - 1)/(-1x - 2))^2 - 1((-3x - 1)/(-1x - 2)) + 3) + 2) + 1))/(3(3cos(1\u03c0(1((-3x - 1)/(-1x - 2))^2 - 1((-3x - 1)/(-1x - 2)) + 3) + 2) + 1) - 1)) + 1| + 2)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4((1((2(-2|(2sin(1\u03c0((1x - 1)/(-1x + 2)) - 2) - 2)| - 3) + 3)/(2(-2|(2sin(1\u03c0((1x - 1)/(-1x + 2)) - 2) - 2)| - 3) - 1)) - 3)/(-2((2(-2|(2sin(1\u03c0((1x - 1)/(-1x + 2)) - 2) - 2)| - 3) + 3)/(2(-2|(2sin(1\u03c0((1x - 1)/(-1x + 2)) - 2) - 2)| - 3) - 1)) - 1)) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(1sin(2\u03c0(4(-3(3((-1x - 2)/(2x + 3)) + 2) - 5) + 4) + 2) - 1) - 2| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(1|(-3|(1e^(1((-2(2x^2 + 5x) + 2)/(-3(2x^2 + 5x))))) - 1|) + 1|) - 3| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2((3(-3|(3cos(1\u03c0(2(-2x + 4)^2 - 1(-2x + 4) - 1) + 1) + 1) - 3| + 3))/(-2(-3|(3cos(1\u03c0(2(-2x + 4)^2 - 1(-2x + 4) - 1) + 1) + 1) - 3| + 3) + 1)) + 1)/(1((3(-3|(3cos(1\u03c0(2(-2x + 4)^2 - 1(-2x + 4) - 1) + 1) + 1) - 3| + 3))/(-2(-3|(3cos(1\u03c0(2(-2x + 4)^2 - 1(-2x + 4) - 1) + 1) + 1) - 3| + 3) + 1))) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(1cos(1\u03c0(5((2(-5(1x^2 - 5x) - 3) + 1)/(2(-5(1x^2 - 5x) - 3) - 3)) + 5) + 1) + 1) + 3| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(2cos(2\u03c0(-2(1(4(-1x + 2)^2 - 1(-1x + 2) - 5)^2 - 1(4(-1x + 2)^2 - 1(-1x + 2) - 5)) - 4) + 2)) - 3)/(-1(2cos(2\u03c0(-2(1(4(-1x + 2)^2 - 1(-1x + 2) - 5)^2 - 1(4(-1x + 2)^2 - 1(-1x + 2) - 5)) - 4) + 2)) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((-2(3cos(3\u03c0((-1(-4(2x + 2) + 3) - 2)/(3(-4(2x + 2) + 3) - 2)) - 3) + 1) - 2)/(-3(3cos(3\u03c0((-1(-4(2x + 2) + 3) - 2)/(3(-4(2x + 2) + 3) - 2)) - 3) + 1) + 1)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(1(-2|(3sin(3\u03c0((-1((-2x + 1)/(3x)) - 1)/(-3((-2x + 1)/(3x)) - 2)) - 2) - 1) - 3| - 2) + 2) + 1| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(3((-2(-1(1sin(3\u03c0(-3x^2 - 2x + 4) - 1))^2 - 3(1sin(3\u03c0(-3x^2 - 2x + 4) - 1)) + 5) - 1)/(2(-1(1sin(3\u03c0(-3x^2 - 2x + 4) - 1))^2 - 3(1sin(3\u03c0(-3x^2 - 2x + 4) - 1)) + 5) + 2)) + 2)^2 + 3(3((-2(-1(1sin(3\u03c0(-3x^2 - 2x + 4) - 1))^2 - 3(1sin(3\u03c0(-3x^2 - 2x + 4) - 1)) + 5) - 1)/(2(-1(1sin(3\u03c0(-3x^2 - 2x + 4) - 1))^2 - 3(1sin(3\u03c0(-3x^2 - 2x + 4) - 1)) + 5) + 2)) + 2) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1((1(-2(-2cos(2\u03c0(-1(5x + 3) - 4) + 2) - 3) - 1) + 2)/(-1(-2(-2cos(2\u03c0(-1(5x + 3) - 4) + 2) - 3) - 1)))^2 + 2((1(-2(-2cos(2\u03c0(-1(5x + 3) - 4) + 2) - 3) - 1) + 2)/(-1(-2(-2cos(2\u03c0(-1(5x + 3) - 4) + 2) - 3) - 1))) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((1(-1cos(2\u03c0(3(2((-1x - 1)/(-1x + 2)) + 5) + 1)) + 2))/(-1(-1cos(2\u03c0(3(2((-1x - 1)/(-1x + 2)) + 5) + 1)) + 2) - 1))^2 - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(2|(-3sin(1\u03c0(5(-2(-1x - 3) + 3) + 1) - 3) + 3) + 1| + 2) + 1)/(1(2|(-3sin(1\u03c0(5(-2(-1x - 3) + 3) + 1) - 3) + 3) + 1| + 2) + 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-3(-2sin(1\u03c0(-3|(4(2|x - 3| + 3)^2 - 5(2|x - 3| + 3) - 4)| + 1)) + 3)^2 + 4(-2sin(1\u03c0(-3|(4(2|x - 3| + 3)^2 - 5(2|x - 3| + 3) - 4)| + 1)) + 3) + 3)| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-1|(-1|((-3(-2sin(2\u03c0(5x) - 2) + 2) + 1)/(-1(-2sin(2\u03c0(5x) - 2) + 2) + 2)) - 2| + 3) + 1| - 3) + 1| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|((-2(-3(1sin(2\u03c0(-2(3x + 5)^2 - 4(3x + 5)) - 1))^2 + 4(1sin(2\u03c0(-2(3x + 5)^2 - 4(3x + 5)) - 1)) + 5) + 2)/(-1(-3(1sin(2\u03c0(-2(3x + 5)^2 - 4(3x + 5)) - 1))^2 + 4(1sin(2\u03c0(-2(3x + 5)^2 - 4(3x + 5)) - 1)) + 5) - 3))| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-3cos(3\u03c0(1(-1|((1((3x + 3)/(-1x - 3)) + 3)/(1((3x + 3)/(-1x - 3)))) + 2| + 3) - 5)) - 2))/(-2(-3cos(3\u03c0(1(-1|((1((3x + 3)/(-1x - 3)) + 3)/(1((3x + 3)/(-1x - 3)))) + 2| + 3) - 5)) - 2) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(-2|(-2(2cos(3\u03c0((1(-5x^2 + 3x) - 3)/(-3(-5x^2 + 3x) - 3)) + 1))^2 - 4(2cos(3\u03c0((1(-5x^2 + 3x) - 3)/(-3(-5x^2 + 3x) - 3)) + 1)) - 1) - 1| - 3)^2 - 4(-2|(-2(2cos(3\u03c0((1(-5x^2 + 3x) - 3)/(-3(-5x^2 + 3x) - 3)) + 1))^2 - 4(2cos(3\u03c0((1(-5x^2 + 3x) - 3)/(-3(-5x^2 + 3x) - 3)) + 1)) - 1) - 1| - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(2|(1|(-4(-3|(-5x^2 + 2x + 3) - 1|) - 5) - 2|) - 1| - 1) - 2)/(-1(2|(1|(-4(-3|(-5x^2 + 2x + 3) - 1|) - 5) - 2|) - 1| - 1) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((-2(3|(-2sin(3\u03c0((-2(4x^2 - 4x - 2) + 2)/(-2(4x^2 - 4x - 2) - 1))) - 3) + 2| - 2) + 2)/(1(3|(-2sin(3\u03c0((-2(4x^2 - 4x - 2) + 2)/(-2(4x^2 - 4x - 2) - 1))) - 3) + 2| - 2))) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(3|((-1(2cos(1\u03c0((3(-2x^2 + 1) + 3)/(-3(-2x^2 + 1) - 1)))) + 3)/(-1(2cos(1\u03c0((3(-2x^2 + 1) + 3)/(-3(-2x^2 + 1) - 1)))) + 2)) + 3| - 1) - 2)/(-1(3|((-1(2cos(1\u03c0((3(-2x^2 + 1) + 3)/(-3(-2x^2 + 1) - 1)))) + 3)/(-1(2cos(1\u03c0((3(-2x^2 + 1) + 3)/(-3(-2x^2 + 1) - 1)))) + 2)) + 3| - 1) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-5(-1cos(2\u03c0(-3|(2|(3x^2 + 5x - 2)| - 3) + 2| - 3) - 2)) + 2) - 2)/(3(-5(-1cos(2\u03c0(-3|(2|(3x^2 + 5x - 2)| - 3) + 2| - 3) - 2)) + 2) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-3|(3|(2|(2(-2sin(2\u03c0x + 2))^2 + 5(-2sin(2\u03c0x + 2)) - 2) + 1| + 1) + 3| - 1) - 3| + 1) + 3)/(2(-3|(3|(2|(2(-2sin(2\u03c0x + 2))^2 + 5(-2sin(2\u03c0x + 2)) - 2) + 1| + 1) + 3| - 1) - 3| + 1) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(3|((-3(2sin(3\u03c0((-2((-1x + 1)/(-3x - 3)) - 1)/(1((-1x + 1)/(-3x - 3)) + 2)) + 2) + 2) + 3)/(-3(2sin(3\u03c0((-2((-1x + 1)/(-3x - 3)) - 1)/(1((-1x + 1)/(-3x - 3)) + 2)) + 2) + 2) - 3)) + 1| + 2)^2 - 5(3|((-3(2sin(3\u03c0((-2((-1x + 1)/(-3x - 3)) - 1)/(1((-1x + 1)/(-3x - 3)) + 2)) + 2) + 2) + 3)/(-3(2sin(3\u03c0((-2((-1x + 1)/(-3x - 3)) - 1)/(1((-1x + 1)/(-3x - 3)) + 2)) + 2) + 2) - 3)) + 1| + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1cos(1\u03c0(1(-1(-4(-2|x + 1| - 2) - 2) + 3) + 3) - 3) - 2)^2 - 4(-1cos(1\u03c0(1(-1(-4(-2|x + 1| - 2) - 2) + 3) + 3) - 3) - 2) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(-4(3sin(1\u03c0(3(-1|(-2|x - 1| + 3) + 3| - 2) - 5) - 3) - 1) + 4) + 3)/(2(-4(3sin(1\u03c0(3(-1|(-2|x - 1| + 3) + 3| - 2) - 5) - 3) - 1) + 4) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(-1(1cos(3\u03c0(-4((3(2x^2 + 3x + 4) - 3)/(2(2x^2 + 3x + 4) - 1))^2 - 2((3(2x^2 + 3x + 4) - 3)/(2(2x^2 + 3x + 4) - 1)) + 5) + 2)) - 2) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(4(1(-1sin(2\u03c0(-5(-1x^2 + 3x - 5)^2 - 1(-1x^2 + 3x - 5) - 4) - 3) + 2)^2 - 2(-1sin(2\u03c0(-5(-1x^2 + 3x - 5)^2 - 1(-1x^2 + 3x - 5) - 4) - 3) + 2) + 1)^2 - 4(1(-1sin(2\u03c0(-5(-1x^2 + 3x - 5)^2 - 1(-1x^2 + 3x - 5) - 4) - 3) + 2)^2 - 2(-1sin(2\u03c0(-5(-1x^2 + 3x - 5)^2 - 1(-1x^2 + 3x - 5) - 4) - 3) + 2) + 1))^2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2((2(-3(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)^2 + 4(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)) + 1)/(-1(-3(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)^2 + 4(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)) - 1)) - 2)/(3((2(-3(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)^2 + 4(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)) + 1)/(-1(-3(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)^2 + 4(-2cos(1\u03c0(1(-1x - 3) - 5) - 2) + 2)) - 1)) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-1(-2sin(3\u03c0((1((-3(-3|x + 2| - 2))/(-3(-3|x + 2| - 2) + 2)) - 3)/(-3((-3(-3|x + 2| - 2))/(-3(-3|x + 2| - 2) + 2)) + 1)) - 2) - 2)^2 + 2(-2sin(3\u03c0((1((-3(-3|x + 2| - 2))/(-3(-3|x + 2| - 2) + 2)) - 3)/(-3((-3(-3|x + 2| - 2))/(-3(-3|x + 2| - 2) + 2)) + 1)) - 2) - 2) + 4) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2cos(3\u03c0(5(5(1((-2x - 3)/(2x - 3)) + 2) + 3)^2 + 2(5(1((-2x - 3)/(2x - 3)) + 2) + 3) - 5)) - 2)^2 - 3(2cos(3\u03c0(5(5(1((-2x - 3)/(2x - 3)) + 2) + 3)^2 + 2(5(1((-2x - 3)/(2x - 3)) + 2) + 3) - 5)) - 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(1(-2|(-4(2sin(1\u03c0((1x + 3)/(1x + 1)) + 3) - 2) - 2) + 1|)^2 + 1(-2|(-4(2sin(1\u03c0((1x + 3)/(1x + 1)) + 3) - 2) - 2) + 1|) + 4) - 2)/(1(1(-2|(-4(2sin(1\u03c0((1x + 3)/(1x + 1)) + 3) - 2) - 2) + 1|)^2 + 1(-2|(-4(2sin(1\u03c0((1x + 3)/(1x + 1)) + 3) - 2) - 2) + 1|) + 4) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1((1(2|(1(-1|(-2sin(1\u03c0x) + 3) - 2|) + 4) + 1| + 1) + 1)/(-1(2|(1(-1|(-2sin(1\u03c0x) + 3) - 2|) + 4) + 1| + 1) - 2)) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-2(-5((1(-2sin(2\u03c0((-1x - 1)/(2x + 3)) - 3) + 3) - 1)/(2(-2sin(2\u03c0((-1x - 1)/(2x + 3)) - 3) + 3) + 2))^2 + 2((1(-2sin(2\u03c0((-1x - 1)/(2x + 3)) - 3) + 3) - 1)/(2(-2sin(2\u03c0((-1x - 1)/(2x + 3)) - 3) + 3) + 2)) - 5) - 2) - 1| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-5(-1((3(-1sin(3\u03c0((-3x + 3)/(-2x - 2)) - 1) + 3) - 3)/(1(-1sin(3\u03c0((-3x + 3)/(-2x - 2)) - 1) + 3) - 2)) + 5) - 4), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((-1(-3cos(1\u03c0(-1(4(-2x^2 + 3x + 3)^2 + 5(-2x^2 + 3x + 3) - 5)^2 - 1(4(-2x^2 + 3x + 3)^2 + 5(-2x^2 + 3x + 3) - 5) + 5) - 1) - 3) - 2)/(-3(-3cos(1\u03c0(-1(4(-2x^2 + 3x + 3)^2 + 5(-2x^2 + 3x + 3) - 5)^2 - 1(4(-2x^2 + 3x + 3)^2 + 5(-2x^2 + 3x + 3) - 5) + 5) - 1) - 3) - 1)) - 1| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(1|(1cos(3\u03c0(-5(1|(2x - 1) + 1| + 1)^2 - 2(1|(2x - 1) + 1| + 1) - 5) - 3) - 3)| - 1))/(3(1|(1cos(3\u03c0(-5(1|(2x - 1) + 1| + 1)^2 - 2(1|(2x - 1) + 1| + 1) - 5) - 3) - 3)| - 1) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(3|((3(1|(3sin(2\u03c0((-3x + 2)/(-1x + 2))))| + 1) - 2)/(-3(1|(3sin(2\u03c0((-3x + 2)/(-1x + 2))))| + 1) + 4)) - 3| - 2)^2 - 3(3|((3(1|(3sin(2\u03c0((-3x + 2)/(-1x + 2))))| + 1) - 2)/(-3(1|(3sin(2\u03c0((-3x + 2)/(-1x + 2))))| + 1) + 4)) - 3| - 2) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-1(-3(-5(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2)^2 - 3(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2))^2 + 3(-5(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2)^2 - 3(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2))) + 1) - 2)/(-3(-1(-3(-5(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2)^2 - 3(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2))^2 + 3(-5(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2)^2 - 3(2cos(2\u03c0(-1|x + 1| - 3) + 3) + 2))) + 1) + 4) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1sin(3\u03c0(-5(3|(-5((-3x + 1)/(-2x + 3)) - 1) - 3| + 1) - 3) - 2) - 1) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2|(3(2cos(2\u03c0((-1((2x + 2)/(-1x)) + 1)/(-2((2x + 2)/(-1x)) - 2))) + 1)^2 - 5(2cos(2\u03c0((-1((2x + 2)/(-1x)) + 1)/(-2((2x + 2)/(-1x)) - 2))) + 1) + 4) - 2| - 2) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(2|(1(3((-2(1|x - 1| + 1) + 3)/(-1(1|x - 1| + 1) + 2))^2 - 4((-2(1|x - 1| + 1) + 3)/(-1(1|x - 1| + 1) + 2)) - 3) + 4)| - 2) + 1)/(3(2|(1(3((-2(1|x - 1| + 1) + 3)/(-1(1|x - 1| + 1) + 2))^2 - 4((-2(1|x - 1| + 1) + 3)/(-1(1|x - 1| + 1) + 2)) - 3) + 4)| - 2)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-3(-5(3cos(1\u03c0(1((-2x - 2)/(3x - 2))^2 + 4((-2x - 2)/(3x - 2)) - 2) + 2) + 1) + 1)^2 - 5(-5(3cos(1\u03c0(1((-2x - 2)/(3x - 2))^2 + 4((-2x - 2)/(3x - 2)) - 2) + 2) + 1) + 1) - 5))/(2(-3(-5(3cos(1\u03c0(1((-2x - 2)/(3x - 2))^2 + 4((-2x - 2)/(3x - 2)) - 2) + 2) + 1) + 1)^2 - 5(-5(3cos(1\u03c0(1((-2x - 2)/(3x - 2))^2 + 4((-2x - 2)/(3x - 2)) - 2) + 2) + 1) + 1) - 5) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3cos(1\u03c0(-1(-3|((-2(1x + 2) + 2)/(3(1x + 2) - 2))| - 2)^2 - 3(-3|((-2(1x + 2) + 2)/(3(1x + 2) - 2))| - 2) + 4) + 1) - 3)| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-1|((1(-3(-2|(3cos(3\u03c0x - 2) + 2) - 3|)^2 + 2(-2|(3cos(3\u03c0x - 2) + 2) - 3|) - 3) + 3)/(-3(-3(-2|(3cos(3\u03c0x - 2) + 2) - 3|)^2 + 2(-2|(3cos(3\u03c0x - 2) + 2) - 3|) - 3))) + 2|)| - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((2(-1(-1sin(2\u03c0(1((1x + 1)/(-1x - 3))^2 + 2((1x + 1)/(-1x - 3)) - 5) - 3) + 2) - 3) + 2)/(2(-1(-1sin(2\u03c0(1((1x + 1)/(-1x - 3))^2 + 2((1x + 1)/(-1x - 3)) - 5) - 3) + 2) - 3)))^2 - 2((2(-1(-1sin(2\u03c0(1((1x + 1)/(-1x - 3))^2 + 2((1x + 1)/(-1x - 3)) - 5) - 3) + 2) - 3) + 2)/(2(-1(-1sin(2\u03c0(1((1x + 1)/(-1x - 3))^2 + 2((1x + 1)/(-1x - 3)) - 5) - 3) + 2) - 3))) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-1((-3((2(-4(2cos(1\u03c0x + 1) + 1) - 4) - 1)/(-1(-4(2cos(1\u03c0x + 1) + 1) - 4) + 2)) + 2)/(-1((2(-4(2cos(1\u03c0x + 1) + 1) - 4) - 1)/(-1(-4(2cos(1\u03c0x + 1) + 1) - 4) + 2)) + 2)) - 2) + 1)/(3(-1((-3((2(-4(2cos(1\u03c0x + 1) + 1) - 4) - 1)/(-1(-4(2cos(1\u03c0x + 1) + 1) - 4) + 2)) + 2)/(-1((2(-4(2cos(1\u03c0x + 1) + 1) - 4) - 1)/(-1(-4(2cos(1\u03c0x + 1) + 1) - 4) + 2)) + 2)) - 2) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-2cos(3\u03c0(3(-3|(-1|(1|x + 3| + 3) - 2| + 1) - 2| - 3) + 2) - 2) - 2)^2 + 4(-2cos(3\u03c0(3(-3|(-1|(1|x + 3| + 3) - 2| + 1) - 2| - 3) + 2) - 2) - 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(-1sin(1\u03c0(-1(1|(2(3x^2 - 2x + 3) + 3) + 3| - 2) + 5) - 2) + 1) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(1sin(3\u03c0(-3((2((2(-1x + 1) + 2)/(1(-1x + 1))) - 3)/(1((2(-1x + 1) + 2)/(1(-1x + 1))) + 2))^2 - 2((2((2(-1x + 1) + 2)/(1(-1x + 1))) - 3)/(1((2(-1x + 1) + 2)/(1(-1x + 1))) + 2)) + 1) - 3) - 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(-2|(-3cos(2\u03c0(2|(4((2x - 2)/(3x + 2))^2 - 4((2x - 2)/(3x + 2)) + 5) + 2|) - 1) + 1) + 1| - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(3sin(1\u03c0((-1(4((-2(-1|x + 3|) + 3)/(-3(-1|x + 3|) - 2)) + 2) + 3)/(-1(4((-2(-1|x + 3|) + 3)/(-3(-1|x + 3|) - 2)) + 2))) + 2) + 3)^2 - 4(3sin(1\u03c0((-1(4((-2(-1|x + 3|) + 3)/(-3(-1|x + 3|) - 2)) + 2) + 3)/(-1(4((-2(-1|x + 3|) + 3)/(-3(-1|x + 3|) - 2)) + 2))) + 2) + 3) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(4(3|(2|(1|(-1sin(3\u03c0x + 3) - 1) + 2| - 1)| + 3) + 2| + 2)^2 + 4(3|(2|(1|(-1sin(3\u03c0x + 3) - 1) + 2| - 1)| + 3) + 2| + 2) + 3) + 3)/(-3(4(3|(2|(1|(-1sin(3\u03c0x + 3) - 1) + 2| - 1)| + 3) + 2| + 2)^2 + 4(3|(2|(1|(-1sin(3\u03c0x + 3) - 1) + 2| - 1)| + 3) + 2| + 2) + 3) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1((-2(-3|(-1|(-3cos(1\u03c0(2|x - 1| - 3) - 2) + 1)|)| + 2) - 3)/(-1(-3|(-1|(-3cos(1\u03c0(2|x - 1| - 3) - 2) + 1)|)| + 2) + 2)) - 3)/(2((-2(-3|(-1|(-3cos(1\u03c0(2|x - 1| - 3) - 2) + 1)|)| + 2) - 3)/(-1(-3|(-1|(-3cos(1\u03c0(2|x - 1| - 3) - 2) + 1)|)| + 2) + 2)) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1(-2cos(2\u03c0(1|((-1(-4x^2 - 1x + 2) - 2)/(1(-4x^2 - 1x + 2) + 1)) - 2| - 3) - 3) - 1)^2 + 5(-2cos(2\u03c0(1|((-1(-4x^2 - 1x + 2) - 2)/(1(-4x^2 - 1x + 2) + 1)) - 2| - 3) - 3) - 1) - 3)^2 - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(3\u03c0(2((-3(4(4(1x)^2 - 1(1x) - 3)^2 + 4(4(1x)^2 - 1(1x) - 3) - 3) + 2)/(-2(4(4(1x)^2 - 1(1x) - 3)^2 + 4(4(1x)^2 - 1(1x) - 3) - 3) - 2))^2 + 1((-3(4(4(1x)^2 - 1(1x) - 3)^2 + 4(4(1x)^2 - 1(1x) - 3) - 3) + 2)/(-2(4(4(1x)^2 - 1(1x) - 3)^2 + 4(4(1x)^2 - 1(1x) - 3) - 3) - 2)) + 1) - 2) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-4(-2((1(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 2)/(-2(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 1))^2 + 2((1(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 2)/(-2(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 1))) + 3)^2 + 1(-4(-2((1(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 2)/(-2(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 1))^2 + 2((1(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 2)/(-2(5(-2cos(1\u03c0x + 3) - 1)^2 + 3(-2cos(1\u03c0x + 3) - 1) + 3) - 1))) + 3) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(1|(-5((-2(-3(2sin(1\u03c0x + 2)) + 1))/(1(-3(2sin(1\u03c0x + 2)) + 1) + 2)) + 3) - 1| + 1) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(-1|(-2sin(3\u03c0((1(-5(1|x - 3| - 1)^2 + 1(1|x - 3| - 1)) + 2)/(1(-5(1|x - 3| - 1)^2 + 1(1|x - 3| - 1)) - 2)) - 1) + 2) + 1| - 2) + 3)/(-1(-1|(-2sin(3\u03c0((1(-5(1|x - 3| - 1)^2 + 1(1|x - 3| - 1)) + 2)/(1(-5(1|x - 3| - 1)^2 + 1(1|x - 3| - 1)) - 2)) - 1) + 2) + 1| - 2) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(-4((3(2(-5(-3cos(3\u03c0x + 2) + 2)^2 - 5(-3cos(3\u03c0x + 2) + 2) - 1) - 5) + 1)/(2(2(-5(-3cos(3\u03c0x + 2) + 2)^2 - 5(-3cos(3\u03c0x + 2) + 2) - 1) - 5) - 3))^2 - 5((3(2(-5(-3cos(3\u03c0x + 2) + 2)^2 - 5(-3cos(3\u03c0x + 2) + 2) - 1) - 5) + 1)/(2(2(-5(-3cos(3\u03c0x + 2) + 2)^2 - 5(-3cos(3\u03c0x + 2) + 2) - 1) - 5) - 3)) - 2) + 1| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((-3(-1(-2|(-3sin(3\u03c0(-4x + 3) - 1) + 1) - 2|)^2 + 1(-2|(-3sin(3\u03c0(-4x + 3) - 1) + 1) - 2|) + 1) - 1)/(2(-1(-2|(-3sin(3\u03c0(-4x + 3) - 1) + 1) - 2|)^2 + 1(-2|(-3sin(3\u03c0(-4x + 3) - 1) + 1) - 2|) + 1) - 1))| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(5((-1(1(1cos(3\u03c0(-5x - 3) - 2))^2 - 1(1cos(3\u03c0(-5x - 3) - 2)) - 5) - 1)/(3(1(1cos(3\u03c0(-5x - 3) - 2))^2 - 1(1cos(3\u03c0(-5x - 3) - 2)) - 5))) - 2)^2 + 3(5((-1(1(1cos(3\u03c0(-5x - 3) - 2))^2 - 1(1cos(3\u03c0(-5x - 3) - 2)) - 5) - 1)/(3(1(1cos(3\u03c0(-5x - 3) - 2))^2 - 1(1cos(3\u03c0(-5x - 3) - 2)) - 5))) - 2) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(2|(3((-1(2sin(1\u03c0(-5x^2 + 5x - 3) + 3) + 1) + 3)/(-1(2sin(1\u03c0(-5x^2 + 5x - 3) + 3) + 1) - 3)) + 5) - 3| + 3) + 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(1|(-2cos(2\u03c0(-1(3(-5x - 2) - 4) + 1) - 2) + 2) - 3| - 2) - 2)/(-3(1|(-2cos(2\u03c0(-1(3(-5x - 2) - 4) + 1) - 2) + 2) - 3| - 2) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1((-3(3|(1(2cos(2\u03c0(5x^2 + 2x) - 2) + 2)^2 + 4(2cos(2\u03c0(5x^2 + 2x) - 2) + 2) + 4)| - 2) + 1)/(-2(3|(1(2cos(2\u03c0(5x^2 + 2x) - 2) + 2)^2 + 4(2cos(2\u03c0(5x^2 + 2x) - 2) + 2) + 4)| - 2) + 3)))/(1((-3(3|(1(2cos(2\u03c0(5x^2 + 2x) - 2) + 2)^2 + 4(2cos(2\u03c0(5x^2 + 2x) - 2) + 2) + 4)| - 2) + 1)/(-2(3|(1(2cos(2\u03c0(5x^2 + 2x) - 2) + 2)^2 + 4(2cos(2\u03c0(5x^2 + 2x) - 2) + 2) + 4)| - 2) + 3)) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-3sin(1\u03c0((-2(-1|(-1(1|x| - 3)^2 + 2(1|x| - 3) + 4) - 2| + 3) + 3)/(1(-1|(-1(1|x| - 3)^2 + 2(1|x| - 3) + 4) - 2| + 3) + 1)) + 1) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3((-2(-1|(2|(-1sin(1\u03c0(-5x - 4) - 3) + 3) + 1| + 1) + 2| - 1) - 2)/(1(-1|(2|(-1sin(1\u03c0(-5x - 4) - 3) + 3) + 1| + 1) + 2| - 1))) + 1)/(3((-2(-1|(2|(-1sin(1\u03c0(-5x - 4) - 3) + 3) + 1| + 1) + 2| - 1) - 2)/(1(-1|(2|(-1sin(1\u03c0(-5x - 4) - 3) + 3) + 1| + 1) + 2| - 1))) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-3(3(3cos(1\u03c0(-3|(5(-2|x + 3| + 3) + 3) + 1| - 3) - 2) - 1) - 5) + 3)/(3(3(3cos(1\u03c0(-3|(5(-2|x + 3| + 3) + 3) + 1| - 3) - 2) - 1) - 5) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3((2(1((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2))^2 - 5((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)) + 4) + 3)/(-1(1((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2))^2 - 5((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)) + 4) + 2)))/(2((2(1((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2))^2 - 5((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)) + 4) + 3)/(-1(1((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2))^2 - 5((-1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)/(1(-1|(-3cos(2\u03c0x - 1) - 1)| - 3) - 2)) + 4) + 2)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(5(-1|(2|(1|(1sin(3\u03c0x - 3) - 3) - 2| - 2) - 1| + 3)|) + 5) - 3| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1sin(2\u03c0(-4(3(-1|(5((1x - 2)/(3x - 2))^2 + 2((1x - 2)/(3x - 2)) + 2) - 3| - 1) - 3) - 3) - 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(2|(2|(2(4(-5x^2 + 2x + 3) - 5)^2 - 4) - 3| + 1) - 1| - 3) + 1)/(-3(2|(2|(2(4(-5x^2 + 2x + 3) - 5)^2 - 4) - 3| + 1) - 1| - 3)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-1sin(3\u03c0((2(4(-2((2x - 1)/(2x + 3)) - 1)^2 - 1(-2((2x - 1)/(2x + 3)) - 1) - 2) - 3)/(3(4(-2((2x - 1)/(2x + 3)) - 1)^2 - 1(-2((2x - 1)/(2x + 3)) - 1) - 2) + 2)) + 1))^2 - 3(-1sin(3\u03c0((2(4(-2((2x - 1)/(2x + 3)) - 1)^2 - 1(-2((2x - 1)/(2x + 3)) - 1) - 2) - 3)/(3(4(-2((2x - 1)/(2x + 3)) - 1)^2 - 1(-2((2x - 1)/(2x + 3)) - 1) - 2) + 2)) + 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(1|(2(1|((2(-1|x - 2| + 2))/(-1(-1|x - 2| + 2) - 3)) - 2| - 1) - 2) - 2| - 1) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4((2(-4(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2)^2 - 1(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2) + 2) + 1)/(-1(-4(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2)^2 - 1(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2) + 2) - 1))^2 + 3((2(-4(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2)^2 - 1(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2) + 2) + 1)/(-1(-4(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2)^2 - 1(3sin(3\u03c0(-4(-5x + 2)^2 - 1(-5x + 2) + 1)) + 2) + 2) - 1)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-1sin(2\u03c0((2(1|((-3(-3|x + 1| - 2) + 1)/(1(-3|x + 1| - 2) - 2)) - 1| - 2) + 3)/(2(1|((-3(-3|x + 1| - 2) + 1)/(1(-3|x + 1| - 2) - 2)) - 1| - 2) - 1)) + 2) + 3)^2 + 1(-1sin(2\u03c0((2(1|((-3(-3|x + 1| - 2) + 1)/(1(-3|x + 1| - 2) - 2)) - 1| - 2) + 3)/(2(1|((-3(-3|x + 1| - 2) + 1)/(1(-3|x + 1| - 2) - 2)) - 1| - 2) - 1)) + 2) + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5((-1(-3|(-2cos(2\u03c0(1|(-1x + 5) + 2| - 2) - 1) - 3) + 3| - 2) + 1)/(-2(-3|(-2cos(2\u03c0(1|(-1x + 5) + 2| - 2) - 1) - 3) + 3| - 2))) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-5(-5((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2))^2 - 2((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2)) + 4)^2 + 4(-5((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2))^2 - 2((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2)) + 4) + 3) + 2)/(1(-5(-5((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2))^2 - 2((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2)) + 4)^2 + 4(-5((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2))^2 - 2((1(4(1x + 5)^2 - 2(1x + 5) - 1) - 1)/(-1(4(1x + 5)^2 - 2(1x + 5) - 1) + 2)) + 4) + 3) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(2(3|(2((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1))^2 - 5((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1)) + 4) - 3|)^2 + 2(3|(2((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1))^2 - 5((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1)) + 4) - 3|) + 2) - 1)/(-2(2(3|(2((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1))^2 - 5((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1)) + 4) - 3|)^2 + 2(3|(2((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1))^2 - 5((-2(-3|x + 2| + 1))/(3(-3|x + 2| + 1) + 1)) + 4) - 3|) + 2) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(1|(-5(-3sin(2\u03c0((-2(-2|x - 1| + 1) - 1)/(-1(-2|x - 1| + 1))) + 3) + 2) + 1) + 1| + 2)^2 + 5(1|(-5(-3sin(2\u03c0((-2(-2|x - 1| + 1) - 1)/(-1(-2|x - 1| + 1))) + 3) + 2) + 1) + 1| + 2) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(3((3(1sin(3\u03c0((3(1|x + 2| - 3))/(-1(1|x + 2| - 3) + 3)) + 3) - 3) - 1)/(-2(1sin(3\u03c0((3(1|x + 2| - 3))/(-1(1|x + 2| - 3) + 3)) + 3) - 3) - 1)) + 2) + 2| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|((-3((1(-1(-3(3|x| - 2) + 1)^2 - 4(-3(3|x| - 2) + 1) - 1))/(1(-1(-3(3|x| - 2) + 1)^2 - 4(-3(3|x| - 2) + 1) - 1) + 3)) - 3)/(2((1(-1(-3(3|x| - 2) + 1)^2 - 4(-3(3|x| - 2) + 1) - 1))/(1(-1(-3(3|x| - 2) + 1)^2 - 4(-3(3|x| - 2) + 1) - 1) + 3)) - 3)) + 1| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|((-2(1|((2(2|(-1cos(2\u03c0x + 2) - 3) + 1| - 2) - 2)/(-3(2|(-1cos(2\u03c0x + 2) - 3) + 1| - 2)))| + 1) + 2)/(2(1|((2(2|(-1cos(2\u03c0x + 2) - 3) + 1| - 2) - 2)/(-3(2|(-1cos(2\u03c0x + 2) - 3) + 1| - 2)))| + 1) + 2)) - 2|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-3(4(-1(1|(2|x - 1|) + 3| - 1) + 5)^2 - 3(-1(1|(2|x - 1|) + 3| - 1) + 5))^2 + 3(4(-1(1|(2|x - 1|) + 3| - 1) + 5)^2 - 3(-1(1|(2|x - 1|) + 3| - 1) + 5)) + 2)^2 - 2(-3(4(-1(1|(2|x - 1|) + 3| - 1) + 5)^2 - 3(-1(1|(2|x - 1|) + 3| - 1) + 5))^2 + 3(4(-1(1|(2|x - 1|) + 3| - 1) + 5)^2 - 3(-1(1|(2|x - 1|) + 3| - 1) + 5)) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2e^(-1(1|(-5(3|(-1(-2x - 1) + 5) - 2| - 2)^2 - 3(3|(-1(-2x - 1) + 5) - 2| - 2) - 2) + 3| + 3)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|((2(2cos(3\u03c0(-5(3|(4x^2 - 4x - 2) - 2| - 1)) - 2) + 2) - 1)/(1(2cos(3\u03c0(-5(3|(4x^2 - 4x - 2) - 2| - 1)) - 2) + 2))) + 3| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(3cos(2\u03c0(-4(1((2(-1x^2 + 4x - 5) + 1)/(1(-1x^2 + 4x - 5) + 2))^2 + 2((2(-1x^2 + 4x - 5) + 1)/(1(-1x^2 + 4x - 5) + 2)))^2 + 3(1((2(-1x^2 + 4x - 5) + 1)/(1(-1x^2 + 4x - 5) + 2))^2 + 2((2(-1x^2 + 4x - 5) + 1)/(1(-1x^2 + 4x - 5) + 2)))) - 3) - 3) + 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1((1(-1sin(1\u03c0(-4(2|((-1x - 3)/(-1x))|) - 3) + 2) - 1) + 1)/(2(-1sin(1\u03c0(-4(2|((-1x - 3)/(-1x))|) - 3) + 2) - 1) - 3))^2 - 4((1(-1sin(1\u03c0(-4(2|((-1x - 3)/(-1x))|) - 3) + 2) - 1) + 1)/(2(-1sin(1\u03c0(-4(2|((-1x - 3)/(-1x))|) - 3) + 2) - 1) - 3)) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1cos(3\u03c0(5(-1((1(-4(2|x - 1| + 3)^2 - 3(2|x - 1| + 3) - 2) - 2)/(1(-4(2|x - 1| + 3)^2 - 3(2|x - 1| + 3) - 2) + 3)) + 2)^2 + 4(-1((1(-4(2|x - 1| + 3)^2 - 3(2|x - 1| + 3) - 2) - 2)/(1(-4(2|x - 1| + 3)^2 - 3(2|x - 1| + 3) - 2) + 3)) + 2) - 5)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2sin(2\u03c0(-5(2((3(1(3|x| - 1) - 3) - 2)/(1(1(3|x| - 1) - 3) + 2))^2 + 4((3(1(3|x| - 1) - 3) - 2)/(1(1(3|x| - 1) - 3) + 2)) - 1) + 2) - 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(1|(-5(-2sin(1\u03c0(1((2x + 2)/(1x - 3)) + 1) + 2) + 3)^2 - 4(-2sin(1\u03c0(1((2x + 2)/(1x - 3)) + 1) + 2) + 3) - 5) - 1|) - 1)/(-1(1|(-5(-2sin(1\u03c0(1((2x + 2)/(1x - 3)) + 1) + 2) + 3)^2 - 4(-2sin(1\u03c0(1((2x + 2)/(1x - 3)) + 1) + 2) + 3) - 5) - 1|)) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(3\u03c0((-3(-1(-4((-1(3|x + 3| - 3) + 1)/(-3(3|x + 3| - 3) - 2)) - 1) - 1) + 3)/(-1(-1(-4((-1(3|x + 3| - 3) + 1)/(-3(3|x + 3| - 3) - 2)) - 1) - 1) - 1))) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2((-2(1(3|(4(3sin(2\u03c0x + 2) - 2) - 3)| + 2) + 3) - 1)/(2(1(3|(4(3sin(2\u03c0x + 2) - 2) - 3)| + 2) + 3) - 3)) - 1)/(1((-2(1(3|(4(3sin(2\u03c0x + 2) - 2) - 3)| + 2) + 3) - 1)/(2(1(3|(4(3sin(2\u03c0x + 2) - 2) - 3)| + 2) + 3) - 3)) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(2|(-3|(4(-3cos(1\u03c0(2|x| - 1) - 2) - 2) + 5) - 2| + 1) + 2| + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-3|((-1((-3(-1(-2sin(2\u03c0x + 3) - 1)^2 - 4(-2sin(2\u03c0x + 3) - 1) + 1) + 1)/(1(-1(-2sin(2\u03c0x + 3) - 1)^2 - 4(-2sin(2\u03c0x + 3) - 1) + 1) + 3)) + 1)/(1((-3(-1(-2sin(2\u03c0x + 3) - 1)^2 - 4(-2sin(2\u03c0x + 3) - 1) + 1) + 1)/(1(-1(-2sin(2\u03c0x + 3) - 1)^2 - 4(-2sin(2\u03c0x + 3) - 1) + 1) + 3)))) - 3| + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2cos(1\u03c0(-2|(-2|(-2|(2x^2 + 1x - 4) + 2| + 3) - 1| + 2) - 2| + 2) - 1)) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(1(-2cos(1\u03c0(-2|((-1(-2x^2 + 1x + 4))/(1(-2x^2 + 1x + 4) - 3)) - 2| - 2) + 1)) + 5)| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(4(-4(1(-1|(-2sin(2\u03c0x + 2) + 2) + 3| + 3) - 5) + 4) - 4) + 1)/(2(4(-4(1(-1|(-2sin(2\u03c0x + 2) + 2) + 3| + 3) - 5) + 4) - 4) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-1(2|(2(-1(2x - 4)^2 - 5(2x - 4) + 2)^2 + 5(-1(2x - 4)^2 - 5(2x - 4) + 2) - 4) + 3|) - 5) + 2| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(3\u03c0(-5(2|(-1|(-5((-3x + 1)/(2x - 1)) + 5) - 2| - 1) - 3| + 1)^2 - 5(2|(-1|(-5((-3x + 1)/(2x - 1)) + 5) - 2| - 1) - 3| + 1) - 3) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(2\u03c0(4(2|(2|(1|(-2|x - 2| - 1)| - 2)| - 1) + 3| + 2) - 2) - 2) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(-3|((-2((1(-2cos(1\u03c0(1x^2 + 5x) - 1)) + 3)/(-1(-2cos(1\u03c0(1x^2 + 5x) - 1)) + 2)) + 2)/(-2((1(-2cos(1\u03c0(1x^2 + 5x) - 1)) + 3)/(-1(-2cos(1\u03c0(1x^2 + 5x) - 1)) + 2)) + 3)) - 3|) - 2| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(2(-3|(-1(-2|(-2|x + 2| + 2)| + 2)^2 - 2(-2|(-2|x + 2| + 2)| + 2) - 2) + 2| + 3) + 5) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(2cos(2\u03c0(1(1(3(-1|x - 1| + 3)^2 + 3)^2 + 1(3(-1|x - 1| + 3)^2 + 3) - 2)) - 3) + 1)^2 - 3(2cos(2\u03c0(1(1(3(-1|x - 1| + 3)^2 + 3)^2 + 1(3(-1|x - 1| + 3)^2 + 3) - 2)) - 3) + 1) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-1(3(-1(1sin(3\u03c0(1x + 1) + 1) + 1)^2 - 3(1sin(3\u03c0(1x + 1) + 1) + 1) + 3)^2 - 3(-1(1sin(3\u03c0(1x + 1) + 1) + 1)^2 - 3(1sin(3\u03c0(1x + 1) + 1) + 1) + 3) + 3) + 2) - 1)/(-2(-1(3(-1(1sin(3\u03c0(1x + 1) + 1) + 1)^2 - 3(1sin(3\u03c0(1x + 1) + 1) + 1) + 3)^2 - 3(-1(1sin(3\u03c0(1x + 1) + 1) + 1)^2 - 3(1sin(3\u03c0(1x + 1) + 1) + 1) + 3) + 3) + 2) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3cos(2\u03c0(1|((3(-1(2|((-1x + 3)/(1x)) - 3| + 3) + 1) + 2)/(-1(-1(2|((-1x + 3)/(1x)) - 3| + 3) + 1) + 2))| + 1) - 1) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(5(2|((-2(1(-1x + 3)^2 - 4(-1x + 3) + 3) + 1)/(-1(1(-1x + 3)^2 - 4(-1x + 3) + 3) - 2)) + 1| - 2))^2 - 5(5(2|((-2(1(-1x + 3)^2 - 4(-1x + 3) + 3) + 1)/(-1(1(-1x + 3)^2 - 4(-1x + 3) + 3) - 2)) + 1| - 2)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(-2|(-2|(2|(-1|(-3|x + 1| + 3)| - 1) + 1| - 1) + 3| + 3) + 3| + 3) + 2)/(-2(-2|(-2|(2|(-1|(-3|x + 1| + 3)| - 1) + 1| - 1) + 3| + 3) + 3| + 3)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(2|((3(3cos(1\u03c0(-1(2x - 2)^2 - 3(2x - 2) - 4) - 2) - 3) - 2)/(1(3cos(1\u03c0(-1(2x - 2)^2 - 3(2x - 2) - 4) - 2) - 3) - 3)) - 2| - 2)^2 - 4(2|((3(3cos(1\u03c0(-1(2x - 2)^2 - 3(2x - 2) - 4) - 2) - 3) - 2)/(1(3cos(1\u03c0(-1(2x - 2)^2 - 3(2x - 2) - 4) - 2) - 3) - 3)) - 2| - 2) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-3|(1(1((-2(1sin(3\u03c0x + 3) + 2) - 3)/(-1(1sin(3\u03c0x + 3) + 2) - 2)) + 5) + 2) + 1| + 2) + 3| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(3sin(3\u03c0(3|(3|((2(5x + 3) - 3)/(-3(5x + 3) + 2)) - 2| + 2) + 3| - 1) + 3)) - 3)/(-2(3sin(3\u03c0(3|(3|((2(5x + 3) - 3)/(-3(5x + 3) + 2)) - 2| + 2) + 3| - 1) + 3)) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|((3(2sin(2\u03c0(-1|(-1(-2|x + 2| + 1) + 5) - 1| - 1) - 1) - 1) - 3)/(-2(2sin(2\u03c0(-1|(-1(-2|x + 2| + 1) + 5) - 1| - 1) - 1) - 1) + 1)) + 3| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-2((3(1(2|(1cos(3\u03c0x - 2) + 1)| - 2) + 4) + 2)/(-2(1(2|(1cos(3\u03c0x - 2) + 1)| - 2) + 4) - 2)) + 3) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(1(-3|(-1|(2(2cos(2\u03c0x + 1))^2 - 1(2cos(2\u03c0x + 1)) - 4)| + 3) + 2| - 3)^2 - 2(-3|(-1|(2(2cos(2\u03c0x + 1))^2 - 1(2cos(2\u03c0x + 1)) - 4)| + 3) + 2| - 3) - 4) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((2(-1|(4(2cos(2\u03c0(4x^2 + 5) - 3) + 3) - 2) + 3| + 3) + 1)/(1(-1|(4(2cos(2\u03c0(4x^2 + 5) - 3) + 3) - 2) + 3| + 3) - 3))^2 + 5((2(-1|(4(2cos(2\u03c0(4x^2 + 5) - 3) + 3) - 2) + 3| + 3) + 1)/(1(-1|(4(2cos(2\u03c0(4x^2 + 5) - 3) + 3) - 2) + 3| + 3) - 3)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(2|(2(-2sin(3\u03c0(-1((-1x + 3)/(1x + 2))^2 + 3((-1x + 3)/(1x + 2)) - 1)) + 3)^2 - 5(-2sin(3\u03c0(-1((-1x + 3)/(1x + 2))^2 + 3((-1x + 3)/(1x + 2)) - 1)) + 3) - 5)| - 2)^2 + 4(2|(2(-2sin(3\u03c0(-1((-1x + 3)/(1x + 2))^2 + 3((-1x + 3)/(1x + 2)) - 1)) + 3)^2 - 5(-2sin(3\u03c0(-1((-1x + 3)/(1x + 2))^2 + 3((-1x + 3)/(1x + 2)) - 1)) + 3) - 5)| - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1((1(2|(-1(4(1cos(3\u03c0x)))^2 - 3(4(1cos(3\u03c0x))) - 4) - 3| + 2) + 3)/(-1(2|(-1(4(1cos(3\u03c0x)))^2 - 3(4(1cos(3\u03c0x))) - 4) - 3| + 2))) - 2)/(1((1(2|(-1(4(1cos(3\u03c0x)))^2 - 3(4(1cos(3\u03c0x))) - 4) - 3| + 2) + 3)/(-1(2|(-1(4(1cos(3\u03c0x)))^2 - 3(4(1cos(3\u03c0x))) - 4) - 3| + 2))) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(1(5((1(5(-1|x| + 1)^2 - 1(-1|x| + 1)) - 2)/(-2(5(-1|x| + 1)^2 - 1(-1|x| + 1)) - 1)) - 4) - 2)^2 - 2(1(5((1(5(-1|x| + 1)^2 - 1(-1|x| + 1)) - 2)/(-2(5(-1|x| + 1)^2 - 1(-1|x| + 1)) - 1)) - 4) - 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|((2(2|((2(-4(-2|x| + 1) - 3) + 2)/(1(-4(-2|x| + 1) - 3))) - 2| - 1) - 3)/(2(2|((2(-4(-2|x| + 1) - 3) + 2)/(1(-4(-2|x| + 1) - 3))) - 2| - 1) + 2)) + 3| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(3(-3cos(1\u03c0(-1(-1|(-4x - 4)| - 1)^2 + 1(-1|(-4x - 4)| - 1) + 5) + 1) + 3)^2 - 2(-3cos(1\u03c0(-1(-1|(-4x - 4)| - 1)^2 + 1(-1|(-4x - 4)| - 1) + 5) + 1) + 3) - 5) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((-3(-5(3cos(3\u03c0((2(-5x^2 - 2x + 5))/(-3(-5x^2 - 2x + 5) + 4)) + 1) + 3) + 2) + 3)/(-2(-5(3cos(3\u03c0((2(-5x^2 - 2x + 5))/(-3(-5x^2 - 2x + 5) + 4)) + 1) + 3) + 2))) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((-2(-1cos(1\u03c0(-2|(1((3x + 3)/(-2x))^2 + 4((3x + 3)/(-2x)) - 2) + 2|) - 1) - 2) + 1)/(-1(-1cos(1\u03c0(-2|(1((3x + 3)/(-2x))^2 + 4((3x + 3)/(-2x)) - 2) + 2|) - 1) - 2) + 2)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2((2(-5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2)^2 - 5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2) + 3) + 1)/(-1(-5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2)^2 - 5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2) + 3) - 2)) - 2)/(-1((2(-5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2)^2 - 5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2) + 3) + 1)/(-1(-5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2)^2 - 5(3|(-2sin(3\u03c0((-3x - 3)/(-2x + 3))) + 3) - 2| + 2) + 3) - 2)) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(-1((-3(1cos(3\u03c0(-3|(3|x - 2| + 2)|)) + 1) + 2)/(2(1cos(3\u03c0(-3|(3|x - 2| + 2)|)) + 1))))^2 - 1(-1((-3(1cos(3\u03c0(-3|(3|x - 2| + 2)|)) + 1) + 2)/(2(1cos(3\u03c0(-3|(3|x - 2| + 2)|)) + 1)))) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(5((1(-4(-1sin(1\u03c0((2x - 2)/(-3x + 2)) - 2) - 2) + 4) - 1)/(3(-4(-1sin(1\u03c0((2x - 2)/(-3x + 2)) - 2) - 2) + 4) + 1)) + 1)^2 - 4(5((1(-4(-1sin(1\u03c0((2x - 2)/(-3x + 2)) - 2) - 2) + 4) - 1)/(3(-4(-1sin(1\u03c0((2x - 2)/(-3x + 2)) - 2) - 2) + 4) + 1)) + 1) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-2|((-1(4(1(1x^2 - 2x - 1) + 1)^2 - 1(1(1x^2 - 2x - 1) + 1) - 1) + 2)/(-2(4(1(1x^2 - 2x - 1) + 1)^2 - 1(1(1x^2 - 2x - 1) + 1) - 1) + 1)) - 2| + 3) - 2| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1((1((-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) + 1)/(-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) - 3)) + 1)/(-3((-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) + 1)/(-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) - 3)) - 2)) + 3)/(-1((1((-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) + 1)/(-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) - 3)) + 1)/(-3((-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) + 1)/(-2((-1(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5))/(-3(-3(1cos(2\u03c0x - 2) - 3)^2 - 4(1cos(2\u03c0x - 2) - 3) + 5) + 4)) - 3)) - 2))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(3(2(-1(-3sin(1\u03c0(3x - 5) - 3) - 2)) - 4) - 4) - 1| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(3|(-2(-3sin(3\u03c0(3|((-3x + 1)/(3x + 3)) - 3| - 1) - 3) + 3) + 2) - 2| - 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(4(3sin(1\u03c0((3(2|(1|x + 3| - 3) - 2| - 2) + 2)/(2(2|(1|x + 3| - 3) - 2| - 2) + 2)) + 3) + 2)^2 + 4(3sin(1\u03c0((3(2|(1|x + 3| - 3) - 2| - 2) + 2)/(2(2|(1|x + 3| - 3) - 2| - 2) + 2)) + 3) + 2) - 2)^2 - 5(4(3sin(1\u03c0((3(2|(1|x + 3| - 3) - 2| - 2) + 2)/(2(2|(1|x + 3| - 3) - 2| - 2) + 2)) + 3) + 2)^2 + 4(3sin(1\u03c0((3(2|(1|x + 3| - 3) - 2| - 2) + 2)/(2(2|(1|x + 3| - 3) - 2| - 2) + 2)) + 3) + 2) - 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|((1(4(2|(2|((3x - 2)/(2x + 3)) - 1| - 1) - 3|) - 4) + 3)/(-1(4(2|(2|((3x - 2)/(2x + 3)) - 1| - 1) - 3|) - 4) - 2)) + 3|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(3|(3sin(2\u03c0(2|(-1(-3x^2 + 4x - 1) - 2) + 3| + 3) + 2) + 2) + 3| - 1) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-1((2(2sin(2\u03c0(2|(-2|x| - 1) - 3| - 2) - 1) + 1) - 1)/(3(2sin(2\u03c0(2|(-2|x| - 1) - 3| - 2) - 1) + 1) + 3)) + 1) - 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(1|(2(-1|(5(-1sin(3\u03c0x - 2) - 2)^2 - 2) + 3| - 3)^2 + 3(-1|(5(-1sin(3\u03c0x - 2) - 2)^2 - 2) + 3| - 3) + 5) - 3| - 2) - 3)/(-1(1|(2(-1|(5(-1sin(3\u03c0x - 2) - 2)^2 - 2) + 3| - 3)^2 + 3(-1|(5(-1sin(3\u03c0x - 2) - 2)^2 - 2) + 3| - 3) + 5) - 3| - 2) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(3((2(-2cos(3\u03c0(1(-1|x - 2| + 3) + 4) + 3) - 3) + 2)/(-2(-2cos(3\u03c0(1(-1|x - 2| + 3) + 4) + 3) - 3) - 1))^2 - 2) - 2)/(-2(3((2(-2cos(3\u03c0(1(-1|x - 2| + 3) + 4) + 3) - 3) + 2)/(-2(-2cos(3\u03c0(1(-1|x - 2| + 3) + 4) + 3) - 3) - 1))^2 - 2) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(2(-2cos(1\u03c0(4((3(1x^2 + 3) + 2)/(2(1x^2 + 3) - 1)) - 1) + 1) - 2) + 4) - 2)/(-3(2(-2cos(1\u03c0(4((3(1x^2 + 3) + 2)/(2(1x^2 + 3) - 1)) - 1) + 1) - 2) + 4) - 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(5(-3|(-1cos(2\u03c0(1|(3x^2 + 1x + 4)| - 2) + 1)) - 2| + 3)^2)| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((2((-3(-2|(-2(-1x^2 - 5x)^2 + 2(-1x^2 - 5x) + 2) - 1| + 2) + 1)/(2(-2|(-2(-1x^2 - 5x)^2 + 2(-1x^2 - 5x) + 2) - 1| + 2) - 1)) + 3)/(2((-3(-2|(-2(-1x^2 - 5x)^2 + 2(-1x^2 - 5x) + 2) - 1| + 2) + 1)/(2(-2|(-2(-1x^2 - 5x)^2 + 2(-1x^2 - 5x) + 2) - 1| + 2) - 1)) + 1)) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(1(2|(5((-2(2cos(3\u03c0x) - 2) - 1)/(2(2cos(3\u03c0x) - 2) - 1))^2 + 1((-2(2cos(3\u03c0x) - 2) - 1)/(2(2cos(3\u03c0x) - 2) - 1)) - 1) - 3|) - 5) + 2| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(3(5((2(-3(-3sin(1\u03c0x + 1) - 3) - 2) - 1)/(-1(-3(-3sin(1\u03c0x + 1) - 3) - 2) + 2)) + 4) - 1) + 3| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(-1(3|((3((-2(1cos(1\u03c0x + 3) - 3) - 1)/(1(1cos(1\u03c0x + 3) - 3) + 3)) - 1)/(-1((-2(1cos(1\u03c0x + 3) - 3) - 1)/(1(1cos(1\u03c0x + 3) - 3) + 3)))) + 1| + 2)^2 + 5(3|((3((-2(1cos(1\u03c0x + 3) - 3) - 1)/(1(1cos(1\u03c0x + 3) - 3) + 3)) - 1)/(-1((-2(1cos(1\u03c0x + 3) - 3) - 1)/(1(1cos(1\u03c0x + 3) - 3) + 3)))) + 1| + 2) - 5) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((-2(-5(-2sin(1\u03c0(5(-4x - 3)^2 + 4(-4x - 3)) + 1) - 1)^2 - 5(-2sin(1\u03c0(5(-4x - 3)^2 + 4(-4x - 3)) + 1) - 1) - 1) - 2)/(-3(-5(-2sin(1\u03c0(5(-4x - 3)^2 + 4(-4x - 3)) + 1) - 1)^2 - 5(-2sin(1\u03c0(5(-4x - 3)^2 + 4(-4x - 3)) + 1) - 1) - 1) + 2)) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(1(1|(-2cos(3\u03c0(-3(-1x + 3) + 2) - 2) + 3) - 3| - 2)^2 - 1(1|(-2cos(3\u03c0(-3(-1x + 3) + 2) - 2) + 3) - 3| - 2) - 3) + 1| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(-2|(-4((-2(-1|(2cos(2\u03c0x) - 1) - 1| + 3) - 1)/(-1(-1|(2cos(2\u03c0x) - 1) - 1| + 3) + 2)) - 3) - 1|) - 3| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|((2((2(-1(1|(-1x^2) + 1| + 1) + 4) + 2)/(2(-1(1|(-1x^2) + 1| + 1) + 4) - 1)) + 3)/(-3((2(-1(1|(-1x^2) + 1| + 1) + 4) + 2)/(2(-1(1|(-1x^2) + 1| + 1) + 4) - 1)))) + 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((2(4((-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) - 1)/(-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) + 3)) + 4) - 1)/(-2(4((-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) - 1)/(-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) + 3)) + 4) - 3))^2 + 1((2(4((-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) - 1)/(-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) + 3)) + 4) - 1)/(-2(4((-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) - 1)/(-1(2(-1|x| + 1)^2 + 5(-1|x| + 1) - 4) + 3)) + 4) - 3)) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2((-2(3sin(3\u03c0(3|((-3((3x + 3)/(1x + 3)) + 3)/(1((3x + 3)/(1x + 3)) + 1))| - 1))) - 3)/(2(3sin(3\u03c0(3|((-3((3x + 3)/(1x + 3)) + 3)/(1((3x + 3)/(1x + 3)) + 1))| - 1))) + 1)) + 3)/(-2((-2(3sin(3\u03c0(3|((-3((3x + 3)/(1x + 3)) + 3)/(1((3x + 3)/(1x + 3)) + 1))| - 1))) - 3)/(2(3sin(3\u03c0(3|((-3((3x + 3)/(1x + 3)) + 3)/(1((3x + 3)/(1x + 3)) + 1))| - 1))) + 1)) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-1cos(3\u03c0(-4((-1(-2|(-2|x - 3| - 1) + 3| - 2) - 3)/(2(-2|(-2|x - 3| - 1) + 3| - 2) + 1))^2 + 4((-1(-2|(-2|x - 3| - 1) + 3| - 2) - 3)/(2(-2|(-2|x - 3| - 1) + 3| - 2) + 1)) + 3) + 2) - 3) - 1)/(1(-1cos(3\u03c0(-4((-1(-2|(-2|x - 3| - 1) + 3| - 2) - 3)/(2(-2|(-2|x - 3| - 1) + 3| - 2) + 1))^2 + 4((-1(-2|(-2|x - 3| - 1) + 3| - 2) - 3)/(2(-2|(-2|x - 3| - 1) + 3| - 2) + 1)) + 3) + 2) - 3) + 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((2(-1cos(1\u03c0(3|(-3((2x - 1)/(-2x - 2))^2 + 4((2x - 1)/(-2x - 2)) + 3)|) + 3)) + 1)/(2(-1cos(1\u03c0(3|(-3((2x - 1)/(-2x - 2))^2 + 4((2x - 1)/(-2x - 2)) + 3)|) + 3)) + 2)) - 3| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(1\u03c0((2(-1(3(-2((-3x - 3)/(3x - 1)))^2 - 2(-2((-3x - 3)/(3x - 1))) - 5) - 5))/(1(-1(3(-2((-3x - 3)/(3x - 1)))^2 - 2(-2((-3x - 3)/(3x - 1))) - 5) - 5) - 3))) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(-2|((2(1sin(3\u03c0(1(-1x - 3)^2 + 5(-1x - 3) - 1) + 2) - 1) - 3)/(1(1sin(3\u03c0(1(-1x - 3)^2 + 5(-1x - 3) - 1) + 2) - 1) - 3)) - 2| - 3) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(2|((1(2((-1(-2x^2 + 5x - 4))/(-1(-2x^2 + 5x - 4) + 2))^2 - 5((-1(-2x^2 + 5x - 4))/(-1(-2x^2 + 5x - 4) + 2)) + 3) + 2)/(3(2((-1(-2x^2 + 5x - 4))/(-1(-2x^2 + 5x - 4) + 2))^2 - 5((-1(-2x^2 + 5x - 4))/(-1(-2x^2 + 5x - 4) + 2)) + 3) - 1)) + 1| - 3) - 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3cos(1\u03c0(-3(3(3|((1(3|x - 2| + 3) + 2)/(2(3|x - 2| + 3))) + 1| + 2)^2 + 5(3|((1(3|x - 2| + 3) + 2)/(2(3|x - 2| + 3))) + 1| + 2) + 4))) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(2|(4(-1(2(1|x - 1| + 1)^2 - 4(1|x - 1| + 1) - 3)^2 - 5(2(1|x - 1| + 1)^2 - 4(1|x - 1| + 1) - 3) - 4)^2 - 2(-1(2(1|x - 1| + 1)^2 - 4(1|x - 1| + 1) - 3)^2 - 5(2(1|x - 1| + 1)^2 - 4(1|x - 1| + 1) - 3) - 4) - 5)| - 1) + 2| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3((-1(-5((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2))^2 - 4((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2)) - 5) - 2)/(3(-5((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2))^2 - 4((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2)) - 5))) + 2)/(1((-1(-5((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2))^2 - 4((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2)) - 5) - 2)/(3(-5((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2))^2 - 4((-1(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 1)/(3(-2(1x^2 + 4x - 1)^2 + 4(1x^2 + 4x - 1) + 5) - 2)) - 5)))) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2\u03c0(1(-2|(-3(3|((2x)/(2x + 2)) - 2| - 1)^2 - 4(3|((2x)/(2x + 2)) - 2| - 1) - 4)| + 2) - 2) + 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|((1(1(1(2cos(2\u03c0((1x - 3)/(3x + 1)) - 2) + 2)^2 - 3(2cos(2\u03c0((1x - 3)/(3x + 1)) - 2) + 2) - 5) - 1) - 2)/(3(1(1(2cos(2\u03c0((1x - 3)/(3x + 1)) - 2) + 2)^2 - 3(2cos(2\u03c0((1x - 3)/(3x + 1)) - 2) + 2) - 5) - 1) - 2)) + 2| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(2cos(1\u03c0(2((-2(3|(2x^2 - 4x - 4) + 2| - 1) + 2)/(1(3|(2x^2 - 4x - 4) + 2| - 1) + 2)) + 3) - 1) - 3)^2 - 1(2cos(1\u03c0(2((-2(3|(2x^2 - 4x - 4) + 2| - 1) + 2)/(1(3|(2x^2 - 4x - 4) + 2| - 1) + 2)) + 3) - 1) - 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(5(-1((-3(-1sin(1\u03c0(2|x + 1| + 2) + 3) + 3))/(-2(-1sin(1\u03c0(2|x + 1| + 2) + 3) + 3) - 2)) + 1) + 1) - 1| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-1((3(-1(1(-2sin(3\u03c0x + 3) - 2)^2 + 5(-2sin(3\u03c0x + 3) - 2) + 2) - 5) + 3)/(3(-1(1(-2sin(3\u03c0x + 3) - 2)^2 + 5(-2sin(3\u03c0x + 3) - 2) + 2) - 5) + 2))^2 + 1((3(-1(1(-2sin(3\u03c0x + 3) - 2)^2 + 5(-2sin(3\u03c0x + 3) - 2) + 2) - 5) + 3)/(3(-1(1(-2sin(3\u03c0x + 3) - 2)^2 + 5(-2sin(3\u03c0x + 3) - 2) + 2) - 5) + 2)) - 3) + 3| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(-4(1(2sin(1\u03c0(-1((3x)/(2x - 1))^2 + 3((3x)/(2x - 1)) - 1) - 1) + 3) - 4) + 1) - 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(5(2|(-2(3(1sin(1\u03c0x + 3) - 1) - 5) + 5) - 2| - 1)^2 - 3(2|(-2(3(1sin(1\u03c0x + 3) - 1) - 5) + 5) - 2| - 1) + 3) - 3)/(-1(5(2|(-2(3(1sin(1\u03c0x + 3) - 1) - 5) + 5) - 2| - 1)^2 - 3(2|(-2(3(1sin(1\u03c0x + 3) - 1) - 5) + 5) - 2| - 1) + 3) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5((1(3(-5(-5(1x - 1)^2 - 5(1x - 1) + 1)^2 + 1(-5(1x - 1)^2 - 5(1x - 1) + 1) + 4)^2 + 3(-5(-5(1x - 1)^2 - 5(1x - 1) + 1)^2 + 1(-5(1x - 1)^2 - 5(1x - 1) + 1) + 4) - 3) + 1)/(-1(3(-5(-5(1x - 1)^2 - 5(1x - 1) + 1)^2 + 1(-5(1x - 1)^2 - 5(1x - 1) + 1) + 4)^2 + 3(-5(-5(1x - 1)^2 - 5(1x - 1) + 1)^2 + 1(-5(1x - 1)^2 - 5(1x - 1) + 1) + 4) - 3) + 2)) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((1(-1|(3(1(-1cos(2\u03c0x + 1) + 2) + 2)^2 - 4(1(-1cos(2\u03c0x + 1) + 2) + 2) - 3) - 2| - 3) + 2)/(2(-1|(3(1(-1cos(2\u03c0x + 1) + 2) + 2)^2 - 4(1(-1cos(2\u03c0x + 1) + 2) + 2) - 3) - 2| - 3) + 3)) - 3| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(5((-2(1sin(2\u03c0(-1(4x^2 + 2x - 2)^2 - 4(4x^2 + 2x - 2) - 1) - 3) + 3) + 2)/(2(1sin(2\u03c0(-1(4x^2 + 2x - 2)^2 - 4(4x^2 + 2x - 2) - 1) - 3) + 3)))) - 2| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1cos(2\u03c0(1|(-3((2((-1x - 2)/(-3x + 1)) + 2)/(-2((-1x - 2)/(-3x + 1)) + 3))^2 - 4((2((-1x - 2)/(-3x + 1)) + 2)/(-2((-1x - 2)/(-3x + 1)) + 3)) + 3) - 3| + 3) - 2) - 2) - 2| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-1(-3cos(2\u03c0(-2(3((-1x + 2)/(2x + 1))^2 - 3((-1x + 2)/(2x + 1)) - 1)^2 + 2(3((-1x + 2)/(2x + 1))^2 - 3((-1x + 2)/(2x + 1)) - 1) + 3)) - 3) - 5) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(-3|(3sin(2\u03c0(-1(-1|((1x + 3)/(1x - 3)) + 2| - 2)^2 - 3(-1|((1x + 3)/(1x - 3)) + 2| - 2))) - 3) - 1| + 1) + 2)/(3(-3|(3sin(2\u03c0(-1(-1|((1x + 3)/(1x - 3)) + 2| - 2)^2 - 3(-1|((1x + 3)/(1x - 3)) + 2| - 2))) - 3) - 1| + 1) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((1(2cos(1\u03c0(1(-4(-5x^2 - 2x - 1)^2 - 2(-5x^2 - 2x - 1) + 5)) - 2) + 1) - 1)/(1(2cos(1\u03c0(1(-4(-5x^2 - 2x - 1)^2 - 2(-5x^2 - 2x - 1) + 5)) - 2) + 1) + 1)) - 1| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|((3(1(1|(3(-1x^2 + 1)^2 + 4(-1x^2 + 1) - 2) + 3| - 3) + 5) + 2)/(-1(1(1|(3(-1x^2 + 1)^2 + 4(-1x^2 + 1) - 2) + 3| - 3) + 5) - 1))| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2|(-5((2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 1)/(-2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 2))^2 + 1((2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 1)/(-2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 2)) - 4) - 2| + 1)^2 + 1(2|(-5((2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 1)/(-2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 2))^2 + 1((2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 1)/(-2(-2cos(2\u03c0((1x + 1)/(1x)) - 1) - 1) - 2)) - 4) - 2| + 1) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2sin(3\u03c0(-1(-1|(1((1(5x - 5) - 1)/(1(5x - 5) + 1))^2 + 3((1(5x - 5) - 1)/(1(5x - 5) + 1)) + 2) + 1| - 2))) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3((3(4(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3)^2 - 5(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3) - 4) - 3)/(-2(4(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3)^2 - 5(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3) - 4) + 3)) + 3)/(-2((3(4(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3)^2 - 5(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3) - 4) - 3)/(-2(4(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3)^2 - 5(2cos(3\u03c0((3(3x) - 3)/(2(3x) - 1)) + 2) + 3) - 4) + 3)) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2\u03c0(-1|(-5(-2((2(1x - 2) + 3)/(-2(1x - 2) + 1))^2 + 5((2(1x - 2) + 3)/(-2(1x - 2) + 1)))^2 + 3(-2((2(1x - 2) + 3)/(-2(1x - 2) + 1))^2 + 5((2(1x - 2) + 3)/(-2(1x - 2) + 1))) - 3) + 2| + 2) - 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(2\u03c0(-3|(2|(-1(3|(1x + 4) - 1| + 3) - 4) + 1| - 2) + 2| - 1) - 2) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(2cos(1\u03c0((2(5(-3(2|x - 2| - 2)^2 + 2(2|x - 2| - 2) + 2)^2 + 5(-3(2|x - 2| - 2)^2 + 2(2|x - 2| - 2) + 2) - 2) - 1)/(-1(5(-3(2|x - 2| - 2)^2 + 2(2|x - 2| - 2) + 2)^2 + 5(-3(2|x - 2| - 2)^2 + 2(2|x - 2| - 2) + 2) - 2) - 1))) - 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1sin(3\u03c0(1|(-3(-5(2|(-2x^2 - 1x - 2) + 2| + 1) + 1) + 2) - 3| + 2) + 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(3\u03c0(1(4(-4(3((-1x + 3)/(-3x + 4)))^2 + 2(3((-1x + 3)/(-3x + 4))) + 1) + 5)^2 + 4)) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-5((-1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3) - 1)/(1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3)))^2 - 2((-1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3) - 1)/(1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3))) + 5)^2 + 5(-5((-1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3) - 1)/(1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3)))^2 - 2((-1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3) - 1)/(1(4(3(3cos(3\u03c0x + 2) + 1) + 2) - 3))) + 5) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-3(1sin(3\u03c0((-1(5((2((2x + 3)/(-1x - 2)) + 3)/(-3((2x + 3)/(-1x - 2)) - 1)) - 5) + 3)/(-2(5((2((2x + 3)/(-1x - 2)) + 3)/(-3((2x + 3)/(-1x - 2)) - 1)) - 5) - 3)) - 1) + 3) - 3)/(2(1sin(3\u03c0((-1(5((2((2x + 3)/(-1x - 2)) + 3)/(-3((2x + 3)/(-1x - 2)) - 1)) - 5) + 3)/(-2(5((2((2x + 3)/(-1x - 2)) + 3)/(-3((2x + 3)/(-1x - 2)) - 1)) - 5) - 3)) - 1) + 3) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1\u03c0(-3(-5((-2((-1(-4x - 2) - 3)/(-1(-4x - 2) + 3)) - 3)/(1((-1(-4x - 2) - 3)/(-1(-4x - 2) + 3)) + 1))^2 - 5)^2 - 1(-5((-2((-1(-4x - 2) - 3)/(-1(-4x - 2) + 3)) - 3)/(1((-1(-4x - 2) - 3)/(-1(-4x - 2) + 3)) + 1))^2 - 5) - 5) - 3) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((-1(2cos(1\u03c0(2(-1((1x - 3)/(-3x - 3))^2 + 1)^2 + 1(-1((1x - 3)/(-3x - 3))^2 + 1) + 2) + 1) + 3) - 2)/(-1(2cos(1\u03c0(2(-1((1x - 3)/(-3x - 3))^2 + 1)^2 + 1(-1((1x - 3)/(-3x - 3))^2 + 1) + 2) + 1) + 3) + 2)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-3|(-1sin(2\u03c0(2|(2|((-1x - 1)/(-1x + 3)) + 3| + 2) + 1| - 2) - 2) - 3) + 3|)^2 + 4(-3|(-1sin(2\u03c0(2|(2|((-1x - 1)/(-1x + 3)) + 3| + 2) + 1| - 2) - 2) - 3) + 3|) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(3|(2(1((-1(-2sin(3\u03c0x) - 2) - 1)/(2(-2sin(3\u03c0x) - 2))) - 5)^2 - 4) + 2| - 3) + 3| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-4(1(-2|(-3|(3x^2 - 3)| + 3) + 2| - 1) - 4) + 3)| + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(1cos(2\u03c0(-1|(3|(2(3x^2 + 4x - 2) + 2) + 3| - 2) - 1| - 2) + 1) + 3) + 1)/(-3(1cos(2\u03c0(-1|(3|(2(3x^2 + 4x - 2) + 2) + 3| - 2) - 1| - 2) + 1) + 3) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((3(1|(2(-4(-1cos(2\u03c0x) - 3)^2 + 3(-1cos(2\u03c0x) - 3) + 4) + 2) - 2| - 1) - 3)/(-3(1|(2(-4(-1cos(2\u03c0x) - 3)^2 + 3(-1cos(2\u03c0x) - 3) + 4) + 2) - 2| - 1) + 2))| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-2(-5(-3cos(2\u03c0(-1(3x^2 - 5x - 5) + 5)) + 2)^2 + 5(-3cos(2\u03c0(-1(3x^2 - 5x - 5) + 5)) + 2) + 2) - 1) - 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1(1(1(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))^2 - 4(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))) + 5)^2 - 4(1(1(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))^2 - 4(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))) + 5) + 1)^2 + 3(1(1(1(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))^2 - 4(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))) + 5)^2 - 4(1(1(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))^2 - 4(3((2x - 3)/(2x + 1))^2 - 4((2x - 3)/(2x + 1)))) + 5) + 1) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2((-2(-4(1(-1|(2cos(1\u03c0x - 1) + 1) + 1| - 3) - 4) - 2) + 1)/(-1(-4(1(-1|(2cos(1\u03c0x - 1) + 1) + 1| - 3) - 4) - 2)))^2 - 3((-2(-4(1(-1|(2cos(1\u03c0x - 1) + 1) + 1| - 3) - 4) - 2) + 1)/(-1(-4(1(-1|(2cos(1\u03c0x - 1) + 1) + 1| - 3) - 4) - 2))) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((-2(4(-3sin(3\u03c0((-1(3|x - 3| + 1) + 3)/(1(3|x - 3| + 1) + 1)) - 1) - 2) + 3) + 1)/(1(4(-3sin(3\u03c0((-1(3|x - 3| + 1) + 3)/(1(3|x - 3| + 1) + 1)) - 1) - 2) + 3) - 2)) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(2((2(-2(1|(3x - 1) - 3| - 1)^2 + 5(1|(3x - 1) - 3| - 1) - 1) + 3)/(-1(-2(1|(3x - 1) - 3| - 1)^2 + 5(1|(3x - 1) - 3| - 1) - 1)))^2 + 1((2(-2(1|(3x - 1) - 3| - 1)^2 + 5(1|(3x - 1) - 3| - 1) - 1) + 3)/(-1(-2(1|(3x - 1) - 3| - 1)^2 + 5(1|(3x - 1) - 3| - 1) - 1))) + 1) - 2| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(1sin(2\u03c0((3(2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3))^2 - 2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3)) - 1) - 1)/(1(2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3))^2 - 2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3)) - 1) - 2))) - 3) + 1)/(2(1sin(2\u03c0((3(2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3))^2 - 2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3)) - 1) - 1)/(1(2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3))^2 - 2((-2(1x^2 - 2x + 2) - 3)/(-2(1x^2 - 2x + 2) + 3)) - 1) - 2))) - 3) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(1((-2(-1(2|(4x + 1) + 3| - 1)^2 + 1(2|(4x + 1) + 3| - 1) + 2) + 1)/(-2(-1(2|(4x + 1) + 3| - 1)^2 + 1(2|(4x + 1) + 3| - 1) + 2) - 3)) - 1) - 1| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(4(1|(1|(-4((-2x + 2)/(1x))^2 - 3((-2x + 2)/(1x)))| + 1) - 2| + 3) - 5) + 2)/(-2(4(1|(1|(-4((-2x + 2)/(1x))^2 - 3((-2x + 2)/(1x)))| + 1) - 2| + 3) - 5) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(3((-3(5(2|(1x^2 + 2x - 5) + 1| - 3)^2 + 1(2|(1x^2 + 2x - 5) + 1| - 3) + 3) + 1)/(1(5(2|(1x^2 + 2x - 5) + 1| - 3)^2 + 1(2|(1x^2 + 2x - 5) + 1| - 3) + 3) - 2))^2 - 2((-3(5(2|(1x^2 + 2x - 5) + 1| - 3)^2 + 1(2|(1x^2 + 2x - 5) + 1| - 3) + 3) + 1)/(1(5(2|(1x^2 + 2x - 5) + 1| - 3)^2 + 1(2|(1x^2 + 2x - 5) + 1| - 3) + 3) - 2)) - 4) - 1| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(2\u03c0(-2(2(-3(2|((1x)/(2x - 1)) - 2| + 3)^2 - 2(2|((1x)/(2x - 1)) - 2| + 3) + 5) - 5) + 5) + 2) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(5(2(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1)^2 + 1(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1) - 5)^2 + 5(2(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1)^2 + 1(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1) - 5) + 3) + 3)/(1(5(2(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1)^2 + 1(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1) - 5)^2 + 5(2(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1)^2 + 1(1sin(3\u03c0(3(-3x^2 + 3x + 1)) - 2) - 1) - 5) + 3) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(1(3((-2(-2|(2cos(3\u03c0x - 2)) + 3|) - 2)/(-3(-2|(2cos(3\u03c0x - 2)) + 3|) + 4)) - 1) - 5))/(-2(1(3((-2(-2|(2cos(3\u03c0x - 2)) + 3|) - 2)/(-3(-2|(2cos(3\u03c0x - 2)) + 3|) + 4)) - 1) - 5) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-2(-3|(4(3sin(3\u03c0((1x + 3)/(3x - 1))) - 1)^2 - 4(3sin(3\u03c0((1x + 3)/(3x - 1))) - 1) + 5)| + 3) - 1) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((2(-1(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1)^2 + 4(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1) + 1) - 3)/(-1(-1(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1)^2 + 4(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1) + 1) - 2))^2 + 1((2(-1(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1)^2 + 4(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1) + 1) - 3)/(-1(-1(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1)^2 + 4(2(2(1sin(2\u03c0x - 1) + 2) - 2) - 1) + 1) - 2)) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(3|(-3(3(3((1x - 3)/(-2x))^2 + 4((1x - 3)/(-2x)) - 2) + 5)) - 3| - 2) - 1| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-2|(-2cos(3\u03c0((-1(3((-2x - 1)/(3x + 2))^2 - 4((-2x - 1)/(3x + 2)) - 2) - 2)/(2(3((-2x - 1)/(3x + 2))^2 - 4((-2x - 1)/(3x + 2)) - 2) - 1)) + 3) + 1) - 3| + 1) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((1((1(-2|(1(-2sin(1\u03c0x + 1) - 1)^2 + 2(-2sin(1\u03c0x + 1) - 1) - 5)| + 3) + 3)/(-1(-2|(1(-2sin(1\u03c0x + 1) - 1)^2 + 2(-2sin(1\u03c0x + 1) - 1) - 5)| + 3) - 1)) + 2)/(3((1(-2|(1(-2sin(1\u03c0x + 1) - 1)^2 + 2(-2sin(1\u03c0x + 1) - 1) - 5)| + 3) + 3)/(-1(-2|(1(-2sin(1\u03c0x + 1) - 1)^2 + 2(-2sin(1\u03c0x + 1) - 1) - 5)| + 3) - 1)) - 2)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((2(-3|(-2|(2(-1x^2 - 1x + 4)^2 + 4(-1x^2 - 1x + 4) + 4) - 3| - 1) - 3| + 3) + 1)/(-1(-3|(-2|(2(-1x^2 - 1x + 4)^2 + 4(-1x^2 - 1x + 4) + 4) - 3| - 1) - 3| + 3) + 3))^2 + 1((2(-3|(-2|(2(-1x^2 - 1x + 4)^2 + 4(-1x^2 - 1x + 4) + 4) - 3| - 1) - 3| + 3) + 1)/(-1(-3|(-2|(2(-1x^2 - 1x + 4)^2 + 4(-1x^2 - 1x + 4) + 4) - 3| - 1) - 3| + 3) + 3)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(2cos(3\u03c0(1(4(2|((1x - 2)/(2x - 3)) + 2|) - 5)^2 - 4(4(2|((1x - 2)/(2x - 3)) + 2|) - 5)) - 1) - 3)^2 - 3(2cos(3\u03c0(1(4(2|((1x - 2)/(2x - 3)) + 2|) - 5)^2 - 4(4(2|((1x - 2)/(2x - 3)) + 2|) - 5)) - 1) - 3) + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-1|(2|(-5(-3|(-1sin(2\u03c0x - 2)) + 1| - 3)^2 + 2(-3|(-1sin(2\u03c0x - 2)) + 1| - 3) - 5) + 1| + 2)| - 3) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(1\u03c0(-3((3(-1(-4(-2|x + 2| + 2) - 3)^2 + 1(-4(-2|x + 2| + 2) - 3) + 2))/(3(-1(-4(-2|x + 2| + 2) - 3)^2 + 1(-4(-2|x + 2| + 2) - 3) + 2) - 1)) + 3) + 2) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(2cos(2\u03c0((-3((-2((1((1x + 2)/(2x - 1)) - 3)/(3((1x + 2)/(2x - 1)) - 2)) + 3)/(1((1((1x + 2)/(2x - 1)) - 3)/(3((1x + 2)/(2x - 1)) - 2)) - 2)) - 2)/(-2((-2((1((1x + 2)/(2x - 1)) - 3)/(3((1x + 2)/(2x - 1)) - 2)) + 3)/(1((1((1x + 2)/(2x - 1)) - 3)/(3((1x + 2)/(2x - 1)) - 2)) - 2)) - 3)) + 2)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(1(-4(-2cos(1\u03c0((-3(2|x + 2| + 1) - 3)/(2(2|x + 2| + 1) - 1)) + 2) + 2) + 3)^2 + 5(-4(-2cos(1\u03c0((-3(2|x + 2| + 1) - 3)/(2(2|x + 2| + 1) - 1)) + 2) + 2) + 3) + 1))/(2(1(-4(-2cos(1\u03c0((-3(2|x + 2| + 1) - 3)/(2(2|x + 2| + 1) - 1)) + 2) + 2) + 3)^2 + 5(-4(-2cos(1\u03c0((-3(2|x + 2| + 1) - 3)/(2(2|x + 2| + 1) - 1)) + 2) + 2) + 3) + 1) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2((-1(-3|(4(5(1|x - 2| - 1))^2 - 3(5(1|x - 2| - 1)) - 4) - 2| + 1) + 2)/(-1(-3|(4(5(1|x - 2| - 1))^2 - 3(5(1|x - 2| - 1)) - 4) - 2| + 1) - 2)) - 1)/(2((-1(-3|(4(5(1|x - 2| - 1))^2 - 3(5(1|x - 2| - 1)) - 4) - 2| + 1) + 2)/(-1(-3|(4(5(1|x - 2| - 1))^2 - 3(5(1|x - 2| - 1)) - 4) - 2| + 1) - 2)) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(2|(-1(1(-2(-2|x| + 2)^2 + 3(-2|x| + 2) + 4))^2 + 4(1(-2(-2|x| + 2)^2 + 3(-2|x| + 2) + 4)) + 4) - 1| - 3)| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(3|(-3(2|(1|(2x - 4)| - 2) + 1| - 3)^2 + 5(2|(1|(2x - 4)| - 2) + 1| - 3) - 2) + 1| - 2) + 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3cos(2\u03c0(1(-1(1|(-3|(3x^2 - 5x + 1) - 2| + 1) + 3|) + 1)^2 + 1(-1(1|(-3|(3x^2 - 5x + 1) - 2| + 1) + 3|) + 1) + 4) + 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(3(2(-4(2(-1cos(2\u03c0x + 2) - 3) + 3)^2 - 5(2(-1cos(2\u03c0x + 2) - 3) + 3) + 5) - 3) - 2) - 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-2|((3(-2(-3|(1e^(1x) + 2) - 3|) - 5) + 2)/(-2(-2(-3|(1e^(1x) + 2) - 3|) - 5) + 3)) - 1| + 3)^2 + 4(-2|((3(-2(-3|(1e^(1x) + 2) - 3|) - 5) + 2)/(-2(-2(-3|(1e^(1x) + 2) - 3|) - 5) + 3)) - 1| + 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(-1|((-1(-3(-1sin(1\u03c0(-3x + 1)) + 1)^2 - 1) - 3)/(-1(-3(-1sin(1\u03c0(-3x + 1)) + 1)^2 - 1) + 2)) - 2| - 3)^2 + 2(-1|((-1(-3(-1sin(1\u03c0(-3x + 1)) + 1)^2 - 1) - 3)/(-1(-3(-1sin(1\u03c0(-3x + 1)) + 1)^2 - 1) + 2)) - 2| - 3) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(3\u03c0(-2(1|(-1(-3|(2|x + 2| + 1) - 3| + 1) - 5) - 2| + 1) + 1) - 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(-2|((1(-4(3(-5x^2 + 4x + 4)^2 + 2(-5x^2 + 4x + 4) - 2)^2 + 2(3(-5x^2 + 4x + 4)^2 + 2(-5x^2 + 4x + 4) - 2) - 5) + 1)/(-3(-4(3(-5x^2 + 4x + 4)^2 + 2(-5x^2 + 4x + 4) - 2)^2 + 2(3(-5x^2 + 4x + 4)^2 + 2(-5x^2 + 4x + 4) - 2) - 5))) + 2| - 3) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(-2|(-3((-1(3cos(3\u03c0(-5x^2 + 4x - 2) + 3) - 2) + 1)/(1(3cos(3\u03c0(-5x^2 + 4x - 2) + 3) - 2) + 2)) - 1) - 3|)| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(3(1(-1cos(1\u03c0(-2|(1x - 4) + 1| - 2) - 1) - 1) - 4)^2 - 2(1(-1cos(1\u03c0(-2|(1x - 4) + 1| - 2) - 1) - 1) - 4) - 3) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(2|(-4(3|(-2(1sin(1\u03c0x - 1))^2 - 1(1sin(1\u03c0x - 1)) - 4) + 1| + 1)^2 - 5(3|(-2(1sin(1\u03c0x - 1))^2 - 1(1sin(1\u03c0x - 1)) - 4) + 1| + 1) + 5) + 3| + 1) + 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(1cos(3\u03c0((-1((2(2((3x - 2)/(-1x + 3)) + 3) + 1)/(-2(2((3x - 2)/(-1x + 3)) + 3) - 2)) - 3)/(2((2(2((3x - 2)/(-1x + 3)) + 3) + 1)/(-2(2((3x - 2)/(-1x + 3)) + 3) - 2)) + 3)) - 2) + 3)^2 + 5(1cos(3\u03c0((-1((2(2((3x - 2)/(-1x + 3)) + 3) + 1)/(-2(2((3x - 2)/(-1x + 3)) + 3) - 2)) - 3)/(2((2(2((3x - 2)/(-1x + 3)) + 3) + 1)/(-2(2((3x - 2)/(-1x + 3)) + 3) - 2)) + 3)) - 2) + 3) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-2cos(3\u03c0(-5(1|(2((-3x - 3)/(-1x + 3)) + 4)| + 2) + 1) + 1) + 1) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(2|(-2cos(3\u03c0(-4((-1((2x + 3)/(1x)) - 1)/(2((2x + 3)/(1x)) - 1))^2 + 5((-1((2x + 3)/(1x)) - 1)/(2((2x + 3)/(1x)) - 1)) - 2)) + 3) + 1| - 3) - 3)/(2(2|(-2cos(3\u03c0(-4((-1((2x + 3)/(1x)) - 1)/(2((2x + 3)/(1x)) - 1))^2 + 5((-1((2x + 3)/(1x)) - 1)/(2((2x + 3)/(1x)) - 1)) - 2)) + 3) + 1| - 3)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(2((3(3(3sin(3\u03c0(5x - 4) - 3)) + 4) + 2)/(-3(3(3sin(3\u03c0(5x - 4) - 3)) + 4) + 2)) + 3)| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-1(-3(-2(5(-2sin(1\u03c0x - 2) - 1) + 2)^2 + 2(5(-2sin(1\u03c0x - 2) - 1) + 2) - 1)^2 - 4(-2(5(-2sin(1\u03c0x - 2) - 1) + 2)^2 + 2(5(-2sin(1\u03c0x - 2) - 1) + 2) - 1) + 5) - 3) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(4((-3(-1|(-3cos(3\u03c0((-1x + 2)/(1x)) + 2) + 1) + 2| - 1) + 3)/(2(-1|(-3cos(3\u03c0((-1x + 2)/(1x)) + 2) + 1) + 2| - 1) - 1))^2 - 3((-3(-1|(-3cos(3\u03c0((-1x + 2)/(1x)) + 2) + 1) + 2| - 1) + 3)/(2(-1|(-3cos(3\u03c0((-1x + 2)/(1x)) + 2) + 1) + 2| - 1) - 1)) + 5) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((-3(-2sin(2\u03c0(2(-5(-2|x - 2| - 2)^2 - 4(-2|x - 2| - 2) - 5)) + 3) + 2) - 2)/(3(-2sin(2\u03c0(2(-5(-2|x - 2| - 2)^2 - 4(-2|x - 2| - 2) - 5)) + 3) + 2) - 1))^2 + 4((-3(-2sin(2\u03c0(2(-5(-2|x - 2| - 2)^2 - 4(-2|x - 2| - 2) - 5)) + 3) + 2) - 2)/(3(-2sin(2\u03c0(2(-5(-2|x - 2| - 2)^2 - 4(-2|x - 2| - 2) - 5)) + 3) + 2) - 1)) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(3|((3(1sin(2\u03c0(3(-3x - 5)^2 + 2(-3x - 5) - 2) + 2) + 3))/(-3(1sin(2\u03c0(3(-3x - 5)^2 + 2(-3x - 5) - 2) + 2) + 3) + 4)) - 3| + 2) + 1| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-2cos(1\u03c0(1|(-5(1|(-2|x|) + 3|)^2 - 2(1|(-2|x|) + 3|) + 2) - 2| + 2)) - 3) + 1)/(1(-2cos(1\u03c0(1|(-5(1|(-2|x|) + 3|)^2 - 2(1|(-2|x|) + 3|) + 2) - 2| + 2)) - 3) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1cos(1\u03c0((-3((1(2|((1((-1x + 3)/(-1x - 1)))/(-1((-1x + 3)/(-1x - 1)) - 1)) - 1| + 3) - 2)/(-1(2|((1((-1x + 3)/(-1x - 1)))/(-1((-1x + 3)/(-1x - 1)) - 1)) - 1| + 3))) - 1)/(1((1(2|((1((-1x + 3)/(-1x - 1)))/(-1((-1x + 3)/(-1x - 1)) - 1)) - 1| + 3) - 2)/(-1(2|((1((-1x + 3)/(-1x - 1)))/(-1((-1x + 3)/(-1x - 1)) - 1)) - 1| + 3))) + 1)) + 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(2(2cos(2\u03c0((-3(3|((-3x - 1)/(-3x)) - 3| + 3) + 3)/(1(3|((-3x - 1)/(-3x)) - 3| + 3) - 3)) + 2) - 1)^2 + 2(2cos(2\u03c0((-3(3|((-3x - 1)/(-3x)) - 3| + 3) + 3)/(1(3|((-3x - 1)/(-3x)) - 3| + 3) - 3)) + 2) - 1) + 5)^2 - 2(2(2cos(2\u03c0((-3(3|((-3x - 1)/(-3x)) - 3| + 3) + 3)/(1(3|((-3x - 1)/(-3x)) - 3| + 3) - 3)) + 2) - 1)^2 + 2(2cos(2\u03c0((-3(3|((-3x - 1)/(-3x)) - 3| + 3) + 3)/(1(3|((-3x - 1)/(-3x)) - 3| + 3) - 3)) + 2) - 1) + 5) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1sin(3\u03c0(4(-1|(2|(5x^2 - 3x - 1) - 2| + 2) - 3|)^2 - 3(-1|(2|(5x^2 - 3x - 1) - 2| + 2) - 3|) + 4) - 3) + 2) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(-4(2((2(2sin(2\u03c0(4x + 5)) - 3) - 1)/(3(2sin(2\u03c0(4x + 5)) - 3) - 1))^2 + 2((2(2sin(2\u03c0(4x + 5)) - 3) - 1)/(3(2sin(2\u03c0(4x + 5)) - 3) - 1)) + 2) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(1sin(2\u03c0(1|(2|(-1(-1|x + 1| + 1) - 5) - 3| + 3) - 2| + 1)) + 3) + 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-1((-1(1(5(2cos(2\u03c0x + 2) + 2) + 2) + 5) - 2)/(3(1(5(2cos(2\u03c0x + 2) + 2) + 2) + 5) - 1)) - 3)^2 - 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1((-1(1cos(2\u03c0(-2|((2(2x + 1) - 1)/(-1(2x + 1) + 2)) - 2| + 3) - 2) + 2) - 3)/(-3(1cos(2\u03c0(-2|((2(2x + 1) - 1)/(-1(2x + 1) + 2)) - 2| + 3) - 2) + 2))) + 3)/(-2((-1(1cos(2\u03c0(-2|((2(2x + 1) - 1)/(-1(2x + 1) + 2)) - 2| + 3) - 2) + 2) - 3)/(-3(1cos(2\u03c0(-2|((2(2x + 1) - 1)/(-1(2x + 1) + 2)) - 2| + 3) - 2) + 2)))) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(-1((-3((2(-2cos(1\u03c0(2x^2 + 4x + 3) - 3)) - 3)/(-3(-2cos(1\u03c0(2x^2 + 4x + 3) - 3)) + 1)) - 2)/(-2((2(-2cos(1\u03c0(2x^2 + 4x + 3) - 3)) - 3)/(-3(-2cos(1\u03c0(2x^2 + 4x + 3) - 3)) + 1)) + 3)) + 4) + 2| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|((2((1(5((2(-3sin(3\u03c0x - 3) - 3))/(2(-3sin(3\u03c0x - 3) - 3) + 1))^2 + 4) - 3)/(-3(5((2(-3sin(3\u03c0x - 3) - 3))/(2(-3sin(3\u03c0x - 3) - 3) + 1))^2 + 4) + 2)) - 2)/(1((1(5((2(-3sin(3\u03c0x - 3) - 3))/(2(-3sin(3\u03c0x - 3) - 3) + 1))^2 + 4) - 3)/(-3(5((2(-3sin(3\u03c0x - 3) - 3))/(2(-3sin(3\u03c0x - 3) - 3) + 1))^2 + 4) + 2)) + 3))| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5((1(-2cos(1\u03c0(3|(-3(3|x + 3|)^2 - 5) + 1| - 1))) + 1)/(-2(-2cos(1\u03c0(3|(-3(3|x + 3|)^2 - 5) + 1| - 1))) - 1)) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(2(3|(4(1|(2x - 4) + 3| - 2)^2 - 1(1|(2x - 4) + 3| - 2) - 2) - 2| - 2) - 5)^2 + 1(2(3|(4(1|(2x - 4) + 3| - 2)^2 - 1(1|(2x - 4) + 3| - 2) - 2) - 2| - 2) - 5) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1|(-3|(-4(-1(-3cos(1\u03c0x + 1) - 2)^2 - 4(-3cos(1\u03c0x + 1) - 2) + 5) - 5) - 2| - 1) + 1| - 1) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1sin(2\u03c0(-4((-1(-3(3(-1|x + 3| + 3) + 4)^2 - 3(3(-1|x + 3| + 3) + 4) + 5) - 3)/(-3(-3(3(-1|x + 3| + 3) + 4)^2 - 3(3(-1|x + 3| + 3) + 4) + 5))) - 2) - 1) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(-1|(-2cos(2\u03c0(-5(-2|(-5x + 2)| + 2) - 5) - 2)) - 1|) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|((-2(-1|(-5(3|(-2cos(3\u03c0x + 3) + 3) - 1| - 2) - 5)| - 3) + 2)/(3(-1|(-5(3|(-2cos(3\u03c0x + 3) + 3) - 1| - 2) - 5)| - 3) - 1)) - 2| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(3|(-1cos(3\u03c0(5(-4(1x^2 - 1x)^2 - 2(1x^2 - 1x) - 5) - 5) + 3) - 3) + 3| + 1) - 1)/(1(3|(-1cos(3\u03c0(5(-4(1x^2 - 1x)^2 - 2(1x^2 - 1x) - 5) - 5) + 3) - 3) + 3| + 1)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-3sin(3\u03c0((1((3(-2(-1|x + 2| + 3) - 2) - 2)/(2(-2(-1|x + 2| + 3) - 2) + 1)) + 2)/(3((3(-2(-1|x + 2| + 3) - 2) - 2)/(2(-2(-1|x + 2| + 3) - 2) + 1)) - 2)) + 1)) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(2sin(3\u03c0((2((1(-5(1x - 1)^2 + 5) + 1)/(1(-5(1x - 1)^2 + 5) - 2)) - 3)/(1((1(-5(1x - 1)^2 + 5) + 1)/(1(-5(1x - 1)^2 + 5) - 2)))) - 3) + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(3((1(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4) + 1)/(2(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4)))^2 + 5((1(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4) + 1)/(2(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4)))))/(-1(3((1(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4) + 1)/(2(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4)))^2 + 5((1(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4) + 1)/(2(1(-1(-1|x|) + 1)^2 - 3(-1(-1|x|) + 1) - 4)))) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5((3(-2sin(1\u03c0(3(1|(2x - 2)| + 2) + 3) + 1) - 2) - 2)/(3(-2sin(1\u03c0(3(1|(2x - 2)| + 2) + 3) + 1) - 2) + 1))^2 + 4((3(-2sin(1\u03c0(3(1|(2x - 2)| + 2) + 3) + 1) - 2) - 2)/(3(-2sin(1\u03c0(3(1|(2x - 2)| + 2) + 3) + 1) - 2) + 1)) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(3((1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) + 2)/(1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) - 3))^2 - 1((1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) + 2)/(1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) - 3)) - 2) + 2)/(-1(3((1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) + 2)/(1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) - 3))^2 - 1((1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) + 2)/(1(1(-3|(-2cos(3\u03c0x)) + 3| - 2)) - 3)) - 2) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(5(3cos(2\u03c0(3|(-4(-5x - 5) - 3)|) + 3)) - 5) - 3|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(5(-3(5(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1)^2 + 1(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1))^2 + 1(5(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1)^2 + 1(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1)) + 5)^2 - 5) - 1)/(-2(5(-3(5(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1)^2 + 1(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1))^2 + 1(5(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1)^2 + 1(4(3cos(2\u03c0x - 2) - 1)^2 + 5(3cos(2\u03c0x - 2) - 1) - 1)) + 5)^2 - 5) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-5(-5(-2(3|(-4x^2 + 5x - 3) + 2| - 1)^2 - 1(3|(-4x^2 + 5x - 3) + 2| - 1) - 1) + 2)^2 + 3(-5(-2(3|(-4x^2 + 5x - 3) + 2| - 1)^2 - 1(3|(-4x^2 + 5x - 3) + 2| - 1) - 1) + 2) - 5) - 3)/(2(-5(-5(-2(3|(-4x^2 + 5x - 3) + 2| - 1)^2 - 1(3|(-4x^2 + 5x - 3) + 2| - 1) - 1) + 2)^2 + 3(-5(-2(3|(-4x^2 + 5x - 3) + 2| - 1)^2 - 1(3|(-4x^2 + 5x - 3) + 2| - 1) - 1) + 2) - 5) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-2(-3(-1(2(3cos(3\u03c0x + 2) + 3)^2 - 5(3cos(3\u03c0x + 2) + 3) - 5) + 5))^2 + 3(-3(-1(2(3cos(3\u03c0x + 2) + 3)^2 - 5(3cos(3\u03c0x + 2) + 3) - 5) + 5)) + 5) + 3)/(2(-2(-3(-1(2(3cos(3\u03c0x + 2) + 3)^2 - 5(3cos(3\u03c0x + 2) + 3) - 5) + 5))^2 + 3(-3(-1(2(3cos(3\u03c0x + 2) + 3)^2 - 5(3cos(3\u03c0x + 2) + 3) - 5) + 5)) + 5) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((-2(-1(-5(2cos(2\u03c0(4x^2 + 1x + 1) + 2)) - 4) - 1) - 1)/(-3(-1(-5(2cos(2\u03c0(4x^2 + 1x + 1) + 2)) - 4) - 1) + 4)) + 3| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(2|(3cos(1\u03c0(-1((3((2x - 3)/(2x)) + 1)/(-3((2x - 3)/(2x)) + 4)) - 1)) + 2) + 3| - 3) - 2| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(2sin(2\u03c0((-1(3|(1|(-1|x - 1| + 1)| - 2) + 2| + 2) + 1)/(-1(3|(1|(-1|x - 1| + 1)| - 2) + 2| + 2) + 2)) + 2) - 3) + 1| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(2sin(2\u03c0(2(4(-2|(-3x + 1) + 2| - 1)^2 - 3(-2|(-3x + 1) + 2| - 1) - 3) + 2) - 3) + 1) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-1|(-5(3(1sin(1\u03c0(2|x + 1| - 1) - 3) - 2) + 5)^2 - 4(3(1sin(1\u03c0(2|x + 1| - 1) - 3) - 2) + 5) - 4) - 2| + 3)| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5((3(-3(2cos(2\u03c0((-2(5x + 3) + 1)/(-1(5x + 3) - 1)) + 1))^2 + 4(2cos(2\u03c0((-2(5x + 3) + 1)/(-1(5x + 3) - 1)) + 1)) - 2) + 2)/(2(-3(2cos(2\u03c0((-2(5x + 3) + 1)/(-1(5x + 3) - 1)) + 1))^2 + 4(2cos(2\u03c0((-2(5x + 3) + 1)/(-1(5x + 3) - 1)) + 1)) - 2))) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(3\u03c0(5(-5((1(-2((1x + 1)/(3x + 2)) + 4) - 1)/(-1(-2((1x + 1)/(3x + 2)) + 4) - 3)) + 1) + 3) + 2) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2sin(1\u03c0(-2(1(-2|(-3|(-2x + 1) + 2| + 3) - 1| + 2)^2 - 1(-2|(-3|(-2x + 1) + 2| + 3) - 1| + 2) - 1) + 2) + 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(-3sin(1\u03c0(1|(2(-2|((-2x - 1)/(-2x + 3)) - 3| - 2)) - 1| + 1) + 1) - 1) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-3sin(1\u03c0(-2((-3(-2|(3|x| - 2) - 1| + 1) - 3)/(1(-2|(3|x| - 2) - 1| + 1))) - 4) + 3) - 3)^2 + 4(-3sin(1\u03c0(-2((-3(-2|(3|x| - 2) - 1| + 1) - 3)/(1(-2|(3|x| - 2) - 1| + 1))) - 4) + 3) - 3) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-1(-4(3sin(3\u03c0(-3|((-3x - 2)/(2x)) + 2| - 3) + 2) + 1) + 4)^2 - 5(-4(3sin(3\u03c0(-3|((-3x - 2)/(2x)) + 2| - 3) + 2) + 1) + 4) - 4) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1cos(1\u03c0(-1|(3(2|((2(-2|x + 3| + 2) - 1)/(-1(-2|x + 3| + 2) - 3)) - 2| + 1) - 5) - 2| + 2) - 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(-2(1(1sin(3\u03c0(-2((-1x - 3)/(2x + 3))) + 2))^2 - 2)^2 + 4(1(1sin(3\u03c0(-2((-1x - 3)/(2x + 3))) + 2))^2 - 2) - 5) + 3)/(-1(-2(1(1sin(3\u03c0(-2((-1x - 3)/(2x + 3))) + 2))^2 - 2)^2 + 4(1(1sin(3\u03c0(-2((-1x - 3)/(2x + 3))) + 2))^2 - 2) - 5) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1((1(-3(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1)^2 + 5(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1) + 1) - 3)/(-3(-3(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1)^2 + 5(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1) + 1) + 2))^2 + 1((1(-3(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1)^2 + 5(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1) + 1) - 3)/(-3(-3(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1)^2 + 5(-1((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1))^2 - 4((-3((3x + 1)/(-3x + 2)) - 3)/(3((3x + 1)/(-3x + 2)) + 1)) + 1) + 1) + 2)) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(5(-3cos(2\u03c0((-3(-3(-4x^2 + 2x + 1)^2 - 3(-4x^2 + 2x + 1) + 3) + 1)/(-1(-3(-4x^2 + 2x + 1)^2 - 3(-4x^2 + 2x + 1) + 3) - 1)) - 1) - 1)^2 - 5(-3cos(2\u03c0((-3(-3(-4x^2 + 2x + 1)^2 - 3(-4x^2 + 2x + 1) + 3) + 1)/(-1(-3(-4x^2 + 2x + 1)^2 - 3(-4x^2 + 2x + 1) + 3) - 1)) - 1) - 1) - 4) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3((3((1(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) + 2)/(-3(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) - 3)) + 3)/(1((1(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) + 2)/(-3(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) - 3)) - 2)) + 1)/(1((3((1(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) + 2)/(-3(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) - 3)) + 3)/(1((1(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) + 2)/(-3(1|(-2cos(1\u03c0(2x^2 - 2x + 4) + 3) + 3) - 2|) - 3)) - 2))) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(-1(-3|(1(2(3cos(2\u03c0x) - 1)^2 + 3(3cos(2\u03c0x) - 1))^2 - 3(2(3cos(2\u03c0x) - 1)^2 + 3(3cos(2\u03c0x) - 1))) - 1| - 1) + 5) - 2| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-1cos(1\u03c0(-3(-2|(1((-3x - 3)/(-2x + 1))^2 - 4((-3x - 3)/(-2x + 1)) - 1) - 1| + 2)^2 + 5) - 3) - 2)^2 + 5(-1cos(1\u03c0(-3(-2|(1((-3x - 3)/(-2x + 1))^2 - 4((-3x - 3)/(-2x + 1)) - 1) - 1| + 2)^2 + 5) - 3) - 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(2\u03c0(2|(1(3(-2|((2x + 1)/(2x + 3)) + 2| + 1) + 2)^2 + 3(3(-2|((2x + 1)/(2x + 3)) + 2| + 1) + 2) - 4) - 2| + 2) + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(2\u03c0(-4(-3|(-2(2|((-1x)/(-1x + 2)) + 2|) + 3) + 3| - 2)^2 + 3(-3|(-2(2|((-1x)/(-1x + 2)) + 2|) + 3) + 3| - 2) - 1) - 3) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1sin(1\u03c0(3(-1(-3|(-3|(1x^2 + 1) - 1| + 1) - 2| + 3) - 4) + 5) + 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((3(3|(3(1(2x^2 - 2x - 1) - 5)^2 + 2(1(2x^2 - 2x - 1) - 5) - 2) - 3|) - 2)/(-3(3|(3(1(2x^2 - 2x - 1) - 5)^2 + 2(1(2x^2 - 2x - 1) - 5) - 2) - 3|) - 1))^2 - 2((3(3|(3(1(2x^2 - 2x - 1) - 5)^2 + 2(1(2x^2 - 2x - 1) - 5) - 2) - 3|) - 2)/(-3(3|(3(1(2x^2 - 2x - 1) - 5)^2 + 2(1(2x^2 - 2x - 1) - 5) - 2) - 3|) - 1)) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(1sin(2\u03c0(2|(3(2|(-3|x| - 3) + 2| - 2)^2 - 1(2|(-3|x| - 3) + 2| - 2) - 4)| + 3)) - 3) + 1)/(1(1sin(2\u03c0(2|(3(2|(-3|x| - 3) + 2| - 2)^2 - 1(2|(-3|x| - 3) + 2| - 2) - 4)| + 3)) - 3) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(4(1cos(3\u03c0(-4((1(-5x - 2) - 3)/(2(-5x - 2) + 1))^2 - 3((1(-5x - 2) - 3)/(2(-5x - 2) + 1)) + 3) - 2))^2 + 5(1cos(3\u03c0(-4((1(-5x - 2) - 3)/(2(-5x - 2) + 1))^2 - 3((1(-5x - 2) - 3)/(2(-5x - 2) + 1)) + 3) - 2)) - 2) + 2)/(1(4(1cos(3\u03c0(-4((1(-5x - 2) - 3)/(2(-5x - 2) + 1))^2 - 3((1(-5x - 2) - 3)/(2(-5x - 2) + 1)) + 3) - 2))^2 + 5(1cos(3\u03c0(-4((1(-5x - 2) - 3)/(2(-5x - 2) + 1))^2 - 3((1(-5x - 2) - 3)/(2(-5x - 2) + 1)) + 3) - 2)) - 2)) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(-2(1sin(3\u03c0((-2(4(1|x + 1| - 2)) + 3)/(3(4(1|x + 1| - 2)))) + 2) - 2)^2 - 3(1sin(3\u03c0((-2(4(1|x + 1| - 2)) + 3)/(3(4(1|x + 1| - 2)))) + 2) - 2) - 5) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-2(1cos(2\u03c0(1|(-3((1x - 2)/(3x)) - 1)| - 1)) - 2) + 2) - 2| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(1|(2|(-1|((-2(-3cos(3\u03c0x) + 3) + 1)/(2(-3cos(3\u03c0x) + 3) + 2)) - 2| - 3) + 2|) - 1| + 3) + 3|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(2(5(-5(1|(1sin(3\u03c0x + 1))|) + 3)^2 - 4(-5(1|(1sin(3\u03c0x + 1))|) + 3) + 3)^2 + 3) + 3| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(4(-2(-4(3|(-1sin(2\u03c0x - 3) - 2) - 2|) + 4) + 2) - 5) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-5(1(-4(-1cos(2\u03c0(-1x^2 + 4x + 5) - 3) - 2)^2 + 5(-1cos(2\u03c0(-1x^2 + 4x + 5) - 3) - 2) + 2) - 3) + 3) + 3| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(2(-1|(-3cos(1\u03c0(4((-2x + 3)/(-1x))^2 - 1((-2x + 3)/(-1x)) - 3) + 1) - 1) - 3| - 1) + 1))/(3(2(-1|(-3cos(1\u03c0(4((-2x + 3)/(-1x))^2 - 1((-2x + 3)/(-1x)) - 3) + 1) - 1) - 3| - 1) + 1) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-2sin(1\u03c0(1(-1|(1((-2x + 3)/(1x))^2 - 3((-2x + 3)/(1x)) + 5) - 2| + 2) + 5) - 2))^2 + 3(-2sin(1\u03c0(1(-1|(1((-2x + 3)/(1x))^2 - 3((-2x + 3)/(1x)) + 5) - 2| + 2) + 5) - 2)) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(-3|(5(2(-2sin(3\u03c0(5x + 2) - 3) + 1)^2 - 4(-2sin(3\u03c0(5x + 2) - 3) + 1) + 3)^2 + 4(2(-2sin(3\u03c0(5x + 2) - 3) + 1)^2 - 4(-2sin(3\u03c0(5x + 2) - 3) + 1) + 3) + 5) + 3| - 3) - 3)/(3(-3|(5(2(-2sin(3\u03c0(5x + 2) - 3) + 1)^2 - 4(-2sin(3\u03c0(5x + 2) - 3) + 1) + 3)^2 + 4(2(-2sin(3\u03c0(5x + 2) - 3) + 1)^2 - 4(-2sin(3\u03c0(5x + 2) - 3) + 1) + 3) + 5) + 3| - 3) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(-2(1|(4((3(3cos(2\u03c0x + 1) - 3) - 3)/(3(3cos(2\u03c0x + 1) - 3) + 1)) + 4) - 3| + 2) + 2) + 1| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4((2(1|(3sin(3\u03c0(-5((3x - 3)/(1x + 3))^2 - 1((3x - 3)/(1x + 3)) + 3) + 2) - 3) - 2| + 1))/(2(1|(3sin(3\u03c0(-5((3x - 3)/(1x + 3))^2 - 1((3x - 3)/(1x + 3)) + 3) + 2) - 3) - 2| + 1) - 3)) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(1|(2(-3(1|(-2x + 5) + 2| - 1)^2 + 2) + 1) - 1| + 3)^2 + 5(1|(2(-3(1|(-2x + 5) + 2| - 1)^2 + 2) + 1) - 1| + 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((-2((-3(-1|(-1cos(2\u03c0(2|x - 1|)) - 2) - 2| - 1) + 2)/(2(-1|(-1cos(2\u03c0(2|x - 1|)) - 2) - 2| - 1))) - 3)/(3((-3(-1|(-1cos(2\u03c0(2|x - 1|)) - 2) - 2| - 1) + 2)/(2(-1|(-1cos(2\u03c0(2|x - 1|)) - 2) - 2| - 1))) + 1)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1((-2((-3(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1))/(1(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1) + 3)) - 2)/(-1((-3(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1))/(1(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1) + 3)) + 2))^2 + 3((-2((-3(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1))/(1(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1) + 3)) - 2)/(-1((-3(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1))/(1(-3((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3))^2 + 2((1(1cos(2\u03c0x - 3) - 2) + 2)/(-2(1cos(2\u03c0x - 3) - 2) - 3)) + 1) + 3)) + 2)) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|((-1(3|(5(3cos(3\u03c0(5x - 3) + 1) + 3) - 2) + 1| + 1) - 1)/(1(3|(5(3cos(3\u03c0(5x - 3) + 1) + 3) - 2) + 1| + 1) + 2)) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1cos(2\u03c0(2(3|(4(3|((-2x - 1)/(2x - 1))| - 3))| + 2)^2 - 3(3|(4(3|((-2x - 1)/(2x - 1))| - 3))| + 2) - 1)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(1((-3(5(-3|(-2sin(3\u03c0x + 1) + 1) - 1| - 3) - 5) + 2)/(2(5(-3|(-2sin(3\u03c0x + 1) + 1) - 1| - 3) - 5) + 3)) - 2) - 2| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-1(1(-2(2|(-1x^2 + 5)| - 2)^2 + 2(2|(-1x^2 + 5)| - 2) - 5) + 4) - 4)^2 - 4(-1(1(-2(2|(-1x^2 + 5)| - 2)^2 + 2(2|(-1x^2 + 5)| - 2) - 5) + 4) - 4) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-4(-3((2((-2(-1sin(3\u03c0x - 1) - 2) + 1)/(1(-1sin(3\u03c0x - 1) - 2) - 3)) - 2)/(-2((-2(-1sin(3\u03c0x - 1) - 2) + 1)/(1(-1sin(3\u03c0x - 1) - 2) - 3)) + 3)) - 1) + 4) + 1)/(2(-4(-3((2((-2(-1sin(3\u03c0x - 1) - 2) + 1)/(1(-1sin(3\u03c0x - 1) - 2) - 3)) - 2)/(-2((-2(-1sin(3\u03c0x - 1) - 2) + 1)/(1(-1sin(3\u03c0x - 1) - 2) - 3)) + 3)) - 1) + 4) + 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-1(3|(4(-1(-1sin(1\u03c0x) - 3) + 3) - 5) - 1| + 1) + 2) - 1)/(-2(-1(3|(4(-1(-1sin(1\u03c0x) - 3) + 3) - 5) - 1| + 1) + 2) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(5(1(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1)^2 + 4(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1) - 4)^2 - 3(1(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1)^2 + 4(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1) - 4) + 1) - 3)/(-2(5(1(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1)^2 + 4(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1) - 4)^2 - 3(1(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1)^2 + 4(3cos(2\u03c0(1(5x^2 + 3x - 1) + 3)) + 1) - 4) + 1) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2cos(3\u03c0(-3(-4(-2((-1x + 2)/(2x + 2))) + 2) + 5)) + 1)^2 - 1(-2cos(3\u03c0(-3(-4(-2((-1x + 2)/(2x + 2))) + 2) + 5)) + 1) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(1((-1(-2|(-1|(3sin(3\u03c0x - 2) - 2) + 3| + 1) - 3| - 1) - 2)/(-1(-2|(-1|(3sin(3\u03c0x - 2) - 2) + 3| + 1) - 3| - 1) - 1)) - 2) - 1)/(1(1((-1(-2|(-1|(3sin(3\u03c0x - 2) - 2) + 3| + 1) - 3| - 1) - 2)/(-1(-2|(-1|(3sin(3\u03c0x - 2) - 2) + 3| + 1) - 3| - 1) - 1)) - 2) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(3\u03c0(3|((-1(-1|(2|((1x + 1)/(-2x + 1)) - 2| - 2) - 2| - 2) - 3)/(2(-1|(2|((1x + 1)/(-2x + 1)) - 2| - 2) - 2| - 2) + 1))| + 1) - 2) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((2((1(4(5(-1|x| + 2)^2 - 3)^2 - 4(5(-1|x| + 2)^2 - 3) - 1) - 2)/(2(4(5(-1|x| + 2)^2 - 3)^2 - 4(5(-1|x| + 2)^2 - 3) - 1) - 1)))/(3((1(4(5(-1|x| + 2)^2 - 3)^2 - 4(5(-1|x| + 2)^2 - 3) - 1) - 2)/(2(4(5(-1|x| + 2)^2 - 3)^2 - 4(5(-1|x| + 2)^2 - 3) - 1) - 1)) - 1)) - 1| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-3|((-1(2cos(1\u03c0(2(-4x + 3)^2 - 1(-4x + 3) + 4) - 3) - 1) + 1)/(-3(2cos(1\u03c0(2(-4x + 3)^2 - 1(-4x + 3) + 4) - 3) - 1) + 4)) - 2| + 3)^2 + 2(-3|((-1(2cos(1\u03c0(2(-4x + 3)^2 - 1(-4x + 3) + 4) - 3) - 1) + 1)/(-3(2cos(1\u03c0(2(-4x + 3)^2 - 1(-4x + 3) + 4) - 3) - 1) + 4)) - 2| + 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((-2(-3(-1cos(3\u03c0(-1|((-2x + 2)/(3x)) + 3| + 2) + 3))^2) - 3)/(3(-3(-1cos(3\u03c0(-1|((-2x + 2)/(3x)) + 3| + 2) + 3))^2) + 2))| - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-1(-4(-1|(1cos(2\u03c0(3x^2 + 1x + 5) + 3)) - 1| - 3) - 5)^2 - 3(-4(-1|(1cos(2\u03c0(3x^2 + 1x + 5) + 3)) - 1| - 3) - 5) + 4) + 2)/(-2(-1(-4(-1|(1cos(2\u03c0(3x^2 + 1x + 5) + 3)) - 1| - 3) - 5)^2 - 3(-4(-1|(1cos(2\u03c0(3x^2 + 1x + 5) + 3)) - 1| - 3) - 5) + 4) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(-1|(-3(3cos(3\u03c0(1(2|x + 2| + 3)^2 + 1(2|x + 2| + 3) - 4)) + 2)^2 - 5(3cos(3\u03c0(1(2|x + 2| + 3)^2 + 1(2|x + 2| + 3) - 4)) + 2) - 4) - 1| + 3) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((3((1(-1|(-1sin(2\u03c0(4x^2 + 3x - 5)) - 1) - 3| - 3) + 1)/(2(-1|(-1sin(2\u03c0(4x^2 + 3x - 5)) - 1) - 3| - 3) - 1)) - 3)/(3((1(-1|(-1sin(2\u03c0(4x^2 + 3x - 5)) - 1) - 3| - 3) + 1)/(2(-1|(-1sin(2\u03c0(4x^2 + 3x - 5)) - 1) - 3| - 3) - 1)) - 2)) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|((1(-4((1(2(3|x + 3|) - 1) + 3)/(2(2(3|x + 3|) - 1) - 3))^2 + 2((1(2(3|x + 3|) - 1) + 3)/(2(2(3|x + 3|) - 1) - 3)) + 1) - 1)/(-3(-4((1(2(3|x + 3|) - 1) + 3)/(2(2(3|x + 3|) - 1) - 3))^2 + 2((1(2(3|x + 3|) - 1) + 3)/(2(2(3|x + 3|) - 1) - 3)) + 1) + 2)) - 3| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(1(3(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2)^2 - 2(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2) + 3)^2 - 5(3(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2)^2 - 2(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2) + 3) - 2) - 3)/(-2(1(3(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2)^2 - 2(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2) + 3)^2 - 5(3(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2)^2 - 2(-1|(-3((-1x + 2)/(2x + 3))^2 - 3((-1x + 2)/(2x + 3)) + 4) + 3| + 2) + 3) - 2)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(-4((-1(4(3|(-1sin(3\u03c0x + 1) - 2) + 2| + 2) + 2) - 1)/(-2(4(3|(-1sin(3\u03c0x + 1) - 2) + 2| + 2) + 2) + 1))^2 + 3((-1(4(3|(-1sin(3\u03c0x + 1) - 2) + 2| + 2) + 2) - 1)/(-2(4(3|(-1sin(3\u03c0x + 1) - 2) + 2| + 2) + 2) + 1)) - 5) + 2| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4((-1(-1(-2sin(3\u03c0(-1(-5x - 3) + 4)) + 1) - 2))/(2(-1(-2sin(3\u03c0(-1(-5x - 3) + 4)) + 1) - 2) + 2)) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-3(1cos(2\u03c0(3|(-5(-5x - 4)^2 + 1(-5x - 4) + 1) + 1| + 1) + 1) + 2)^2 - 1(1cos(2\u03c0(3|(-5(-5x - 4)^2 + 1(-5x - 4) + 1) + 1| + 1) + 1) + 2) - 3) - 1)/(3(-3(1cos(2\u03c0(3|(-5(-5x - 4)^2 + 1(-5x - 4) + 1) + 1| + 1) + 1) + 2)^2 - 1(1cos(2\u03c0(3|(-5(-5x - 4)^2 + 1(-5x - 4) + 1) + 1| + 1) + 1) + 2) - 3)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-2|((3(2cos(3\u03c0((3(1|x - 2|) - 1)/(-2(1|x - 2|) - 2)) + 2) - 2) - 3)/(-1(2cos(3\u03c0((3(1|x - 2|) - 1)/(-2(1|x - 2|) - 2)) + 2) - 2) + 2)) + 3|))/(1(-2|((3(2cos(3\u03c0((3(1|x - 2|) - 1)/(-2(1|x - 2|) - 2)) + 2) - 2) - 3)/(-1(2cos(3\u03c0((3(1|x - 2|) - 1)/(-2(1|x - 2|) - 2)) + 2) - 2) + 2)) + 3|) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-1|(-2(-3|(-1|(-1x - 4) - 3| + 3) - 3|)^2 - 3(-3|(-1|(-1x - 4) - 3| + 3) - 3|) + 4)|) + 3| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(3|(-2|(-5(4(2cos(2\u03c0x + 2) - 1)^2 + 3(2cos(2\u03c0x + 2) - 1) - 4)^2 + 5(4(2cos(2\u03c0x + 2) - 1)^2 + 3(2cos(2\u03c0x + 2) - 1) - 4) + 1) - 3| - 2)| + 3) + 1)/(-2(3|(-2|(-5(4(2cos(2\u03c0x + 2) - 1)^2 + 3(2cos(2\u03c0x + 2) - 1) - 4)^2 + 5(4(2cos(2\u03c0x + 2) - 1)^2 + 3(2cos(2\u03c0x + 2) - 1) - 4) + 1) - 3| - 2)| + 3) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2((-1(1(-4(-2sin(1\u03c0(1x - 1) - 3) + 2) - 4) + 4) + 1)/(2(1(-4(-2sin(1\u03c0(1x - 1) - 3) + 2) - 4) + 4) + 2)) + 2)/(1((-1(1(-4(-2sin(1\u03c0(1x - 1) - 3) + 2) - 4) + 4) + 1)/(2(1(-4(-2sin(1\u03c0(1x - 1) - 3) + 2) - 4) + 4) + 2)) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((1((2(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2) + 1)/(1(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2) + 2)))/(2((2(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2) + 1)/(1(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2) + 2)) - 1))| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2((-2(2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3)^2 + 2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3) + 5) - 1)/(3(2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3)^2 + 2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3) + 5)))^2 - 1((-2(2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3)^2 + 2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3) + 5) - 1)/(3(2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3)^2 + 2(3(-3|(-3cos(1\u03c0x + 1) + 1)| - 3) - 3) + 5))) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(-1sin(2\u03c0(-1(1((-2(-1x^2 - 4x + 5) + 1)/(2(-1x^2 - 4x + 5) + 1))^2 + 2((-2(-1x^2 - 4x + 5) + 1)/(2(-1x^2 - 4x + 5) + 1)) - 3)^2 - 5(1((-2(-1x^2 - 4x + 5) + 1)/(2(-1x^2 - 4x + 5) + 1))^2 + 2((-2(-1x^2 - 4x + 5) + 1)/(2(-1x^2 - 4x + 5) + 1)) - 3)) + 3) + 2) + 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3sin(2\u03c0((-1(1(3|(2(-1x^2 + 4x + 1) + 4) + 2| + 1) - 5) + 1)/(1(1(3|(2(-1x^2 + 4x + 1) + 4) + 2| + 1) - 5) - 2)) + 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(-1|((-2(-1cos(1\u03c0(-2|((-3x - 3)/(-3x + 4)) + 3| + 2) + 2) + 1) - 2)/(1(-1cos(1\u03c0(-2|((-3x - 3)/(-3x + 4)) + 3| + 2) + 2) + 1) - 2)) + 2| - 2))/(1(-1|((-2(-1cos(1\u03c0(-2|((-3x - 3)/(-3x + 4)) + 3| + 2) + 2) + 1) - 2)/(1(-1cos(1\u03c0(-2|((-3x - 3)/(-3x + 4)) + 3| + 2) + 2) + 1) - 2)) + 2| - 2) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(1((2(-5(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1)^2 - 1(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1) - 4) - 2)/(-2(-5(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1)^2 - 1(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1) - 4)))^2 + 5((2(-5(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1)^2 - 1(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1) - 4) - 2)/(-2(-5(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1)^2 - 1(3(1cos(3\u03c0x + 1))^2 - 1(1cos(3\u03c0x + 1)) + 1) - 4))) - 1) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2((2(2(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1)^2 + 1(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1) - 4) - 1)/(2(2(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1)^2 + 1(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1) - 4))) - 2)/(2((2(2(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1)^2 + 1(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1) - 4) - 1)/(2(2(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1)^2 + 1(-3cos(3\u03c0(-2|(4x^2 - 3x) - 1| - 1)) - 1) - 4))) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(-2(-3e^(-1((1(3|(1|x - 3| + 1) - 3| - 3) + 1)/(1(3|(1|x - 3| + 1) - 3| - 3) + 2))) + 1)^2 - 2(-3e^(-1((1(3|(1|x - 3| + 1) - 3| - 3) + 1)/(1(3|(1|x - 3| + 1) - 3| - 3) + 2))) + 1) + 1) - 2)/(-1(-2(-3e^(-1((1(3|(1|x - 3| + 1) - 3| - 3) + 1)/(1(3|(1|x - 3| + 1) - 3| - 3) + 2))) + 1)^2 - 2(-3e^(-1((1(3|(1|x - 3| + 1) - 3| - 3) + 1)/(1(3|(1|x - 3| + 1) - 3| - 3) + 2))) + 1) + 1) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(-4((1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5))/(1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5) + 2))^2 + 4((1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5))/(1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5) + 2)) + 5)^2 + 3(-4((1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5))/(1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5) + 2))^2 + 4((1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5))/(1(2((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1))^2 - 4((-2(-1sin(3\u03c0x + 2) - 3) + 1)/(-1(-1sin(3\u03c0x + 2) - 3) - 1)) + 5) + 2)) + 5) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-1(-2|(1cos(2\u03c0(-3|(-1x^2 + 1x) + 2| - 2) - 3) + 3)|)^2 + 1(-2|(1cos(2\u03c0(-3|(-1x^2 + 1x) + 2| - 2) - 3) + 3)|) - 4) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1((-3(4(-1cos(2\u03c0(1(4x^2 + 2x - 3)^2 + 2(4x^2 + 2x - 3)))) + 5) + 1)/(-1(4(-1cos(2\u03c0(1(4x^2 + 2x - 3)^2 + 2(4x^2 + 2x - 3)))) + 5) - 3)) - 2)/(-1((-3(4(-1cos(2\u03c0(1(4x^2 + 2x - 3)^2 + 2(4x^2 + 2x - 3)))) + 5) + 1)/(-1(4(-1cos(2\u03c0(1(4x^2 + 2x - 3)^2 + 2(4x^2 + 2x - 3)))) + 5) - 3)) + 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(2|(-1|(1|(3cos(2\u03c0(4x + 2)) - 2) + 1| + 1) + 2| - 1) - 2| + 2)^2 - 2(2|(-1|(1|(3cos(2\u03c0(4x + 2)) - 2) + 1| + 1) + 2| - 1) - 2| + 2) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(2|((-3(1|(-1sin(1\u03c0((1x)/(2x - 1)) + 1) - 1) + 3| - 1) + 3)/(-1(1|(-1sin(1\u03c0((1x)/(2x - 1)) + 1) - 1) + 3| - 1) - 2)) - 2| + 2) - 3| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(1cos(2\u03c0(3(-3((1(4x^2 + 1x + 1) + 1)/(1(4x^2 + 1x + 1) + 2)) - 2)) + 2) - 1) + 2| - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3((-1(-5(-2sin(2\u03c0(-1(2x)^2 - 3(2x) + 1) - 3) + 2)^2 + 2(-2sin(2\u03c0(-1(2x)^2 - 3(2x) + 1) - 3) + 2) + 4) - 2)/(2(-5(-2sin(2\u03c0(-1(2x)^2 - 3(2x) + 1) - 3) + 2)^2 + 2(-2sin(2\u03c0(-1(2x)^2 - 3(2x) + 1) - 3) + 2) + 4) - 3)) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-5(-3(2cos(2\u03c0(1|(-2x^2 + 3x - 3) + 1| - 3) - 3))^2 + 2(2cos(2\u03c0(1|(-2x^2 + 3x - 3) + 1| - 3) - 3)))^2 + 5(-3(2cos(2\u03c0(1|(-2x^2 + 3x - 3) + 1| - 3) - 3))^2 + 2(2cos(2\u03c0(1|(-2x^2 + 3x - 3) + 1| - 3) - 3))) + 5) + 3| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-3(-4(4((-1(2(-2cos(1\u03c0x + 1) + 2)^2 + 5(-2cos(1\u03c0x + 1) + 2) + 5) - 3)/(-2(2(-2cos(1\u03c0x + 1) + 2)^2 + 5(-2cos(1\u03c0x + 1) + 2) + 5) - 3)) - 5) + 3))/(2(-4(4((-1(2(-2cos(1\u03c0x + 1) + 2)^2 + 5(-2cos(1\u03c0x + 1) + 2) + 5) - 3)/(-2(2(-2cos(1\u03c0x + 1) + 2)^2 + 5(-2cos(1\u03c0x + 1) + 2) + 5) - 3)) - 5) + 3) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3sin(2\u03c0((2(5(-5((1(-2|x - 1| + 1) + 2)/(-3(-2|x - 1| + 1) + 4)))^2 - 5(-5((1(-2|x - 1| + 1) + 2)/(-3(-2|x - 1| + 1) + 4))) - 1) + 3)/(-1(5(-5((1(-2|x - 1| + 1) + 2)/(-3(-2|x - 1| + 1) + 4)))^2 - 5(-5((1(-2|x - 1| + 1) + 2)/(-3(-2|x - 1| + 1) + 4))) - 1) + 2)) + 2) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((1((1(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) + 2)/(2(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) - 1)) + 2)/(-3((1(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) + 2)/(2(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) - 1)) - 2))^2 + 2((1((1(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) + 2)/(2(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) - 1)) + 2)/(-3((1(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) + 2)/(2(-1|(-2(2|x - 2|)^2 - 2(2|x - 2|) + 2) - 1| + 3) - 1)) - 2)) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((-2(-2|(-3cos(3\u03c0(4(3x + 2) + 5) + 2) - 3) - 2| - 2) + 2)/(-3(-2|(-3cos(3\u03c0(4(3x + 2) + 5) + 2) - 3) - 2| - 2) + 4)) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(1|(1(3(1|(3|x + 1| - 3)| + 1) - 4) - 1) + 1|) - 3| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1((-1(-4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2)^2 - 4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2) - 2) - 1)/(1(-4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2)^2 - 4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2) - 2))) + 2)/(3((-1(-4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2)^2 - 4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2) - 2) - 1)/(1(-4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2)^2 - 4(-1|((3(4x^2 - 3x - 4) + 2)/(-2(4x^2 - 3x - 4) + 3)) + 3| + 2) - 2))) + 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((2((-1(-3|(1(1cos(1\u03c0x - 1) + 3)) - 3| - 1) - 1)/(-1(-3|(1(1cos(1\u03c0x - 1) + 3)) - 3| - 1))) + 3)/(-1((-1(-3|(1(1cos(1\u03c0x - 1) + 3)) - 3| - 1) - 1)/(-1(-3|(1(1cos(1\u03c0x - 1) + 3)) - 3| - 1))))) - 1| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(1\u03c0(-2(4((-2(3|(-3x - 2) - 3|) - 3)/(1(3|(-3x - 2) - 3|) - 3))^2 + 2((-2(3|(-3x - 2) - 3|) - 3)/(1(3|(-3x - 2) - 3|) - 3)))^2 + 2(4((-2(3|(-3x - 2) - 3|) - 3)/(1(3|(-3x - 2) - 3|) - 3))^2 + 2((-2(3|(-3x - 2) - 3|) - 3)/(1(3|(-3x - 2) - 3|) - 3))) - 5) + 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-1cos(3\u03c0(-1((-1(1|(-2x + 5) - 2| + 2) - 1)/(-2(1|(-2x + 5) - 2| + 2) + 3))^2 - 2((-1(1|(-2x + 5) - 2| + 2) - 1)/(-2(1|(-2x + 5) - 2| + 2) + 3)) - 2) + 2)) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2cos(1\u03c0(2|(-4(4(5((-2x - 1)/(3x - 2))^2 - 5((-2x - 1)/(3x - 2)) - 5) + 5) + 5) - 3|)) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(2\u03c0(1|(2(-1|(5(-1x - 1) + 4) + 2| - 3)^2 + 1(-1|(5(-1x - 1) + 4) + 2| - 3) + 4) - 2| + 3) - 2) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-3cos(1\u03c0(-3(1(-3((1x + 3)/(-3x + 1)) - 2)^2 - 2(-3((1x + 3)/(-3x + 1)) - 2) + 2)^2 - 4) + 1) + 2) - 3)/(2(-3cos(1\u03c0(-3(1(-3((1x + 3)/(-3x + 1)) - 2)^2 - 2(-3((1x + 3)/(-3x + 1)) - 2) + 2)^2 - 4) + 1) + 2) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3((-2(-1(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2)^2 - 3(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2) + 4) - 1)/(-1(-1(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2)^2 - 3(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2) + 4) + 3)))/(-1((-2(-1(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2)^2 - 3(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2) + 4) - 1)/(-1(-1(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2)^2 - 3(1sin(3\u03c0(2((-3x - 1)/(-3x))^2 + 5((-3x - 1)/(-3x)) - 1) - 2) + 2) + 4) + 3)) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-2|(1(-2cos(3\u03c0((-2(-1x + 4))/(-1(-1x + 4) - 2)) + 3) + 2)^2 - 5(-2cos(3\u03c0((-2(-1x + 4))/(-1(-1x + 4) - 2)) + 3) + 2) + 5) + 1| + 3) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(-1sin(1\u03c0((2(-3|(-1(-1x^2 + 4x + 4) - 4) - 3| + 2) + 2)/(2(-3|(-1(-1x^2 + 4x + 4) - 4) - 3| + 2) - 1)) - 1) - 3) + 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1((1(-1(1|(-3x + 5) - 2| - 3)^2 - 2(1|(-3x + 5) - 2| - 3) + 1) - 2)/(3(-1(1|(-3x + 5) - 2| - 3)^2 - 2(1|(-3x + 5) - 2| - 3) + 1))) + 3)^2 + 4(1((1(-1(1|(-3x + 5) - 2| - 3)^2 - 2(1|(-3x + 5) - 2| - 3) + 1) - 2)/(3(-1(1|(-3x + 5) - 2| - 3)^2 - 2(1|(-3x + 5) - 2| - 3) + 1))) + 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(2|(1((-3(-1(-1|x| - 3) - 3) + 1)/(2(-1(-1|x| - 3) - 3) - 1))^2 - 4((-3(-1(-1|x| - 3) - 3) + 1)/(2(-1(-1|x| - 3) - 3) - 1)) - 2) - 2| - 3)^2 - 1(2|(1((-3(-1(-1|x| - 3) - 3) + 1)/(2(-1(-1|x| - 3) - 3) - 1))^2 - 4((-3(-1(-1|x| - 3) - 3) + 1)/(2(-1(-1|x| - 3) - 3) - 1)) - 2) - 2| - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(1\u03c0((2((-2(-4(2|((1x - 3)/(-3x + 1))| - 3)^2 + 3(2|((1x - 3)/(-3x + 1))| - 3) - 2) - 1)/(2(-4(2|((1x - 3)/(-3x + 1))| - 3)^2 + 3(2|((1x - 3)/(-3x + 1))| - 3) - 2) + 2)) + 3)/(2((-2(-4(2|((1x - 3)/(-3x + 1))| - 3)^2 + 3(2|((1x - 3)/(-3x + 1))| - 3) - 2) - 1)/(2(-4(2|((1x - 3)/(-3x + 1))| - 3)^2 + 3(2|((1x - 3)/(-3x + 1))| - 3) - 2) + 2)) + 2)) + 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-1|(-4(1|(-1cos(1\u03c0(-1x^2 + 4x + 1) + 1) - 1) - 2|) + 1) + 3| - 3) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2cos(2\u03c0(-3(-1(2(2|((-3x + 3)/(1x)) - 3| + 2) - 1)^2 + 3(2(2|((-3x + 3)/(1x)) - 3| + 2) - 1) - 3) + 3) + 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(2(-2|(-4(1|((3x - 2)/(3x + 2)) - 1| - 3) - 2) - 3| + 2)^2 + 5(-2|(-4(1|((3x - 2)/(3x + 2)) - 1| - 3) - 2) - 3| + 2) + 1) + 3)/(1(2(-2|(-4(1|((3x - 2)/(3x + 2)) - 1| - 3) - 2) - 3| + 2)^2 + 5(-2|(-4(1|((3x - 2)/(3x + 2)) - 1| - 3) - 2) - 3| + 2) + 1) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(3|((-3(-2|(-4(2cos(1\u03c0x + 2) + 2)^2 - 4(2cos(1\u03c0x + 2) + 2) - 1) + 3| + 2))/(-1(-2|(-4(2cos(1\u03c0x + 2) + 2)^2 - 4(2cos(1\u03c0x + 2) + 2) - 1) + 3| + 2) - 2)) - 1| + 1) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1((-1(-3((1(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1))/(3(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1) + 3)) + 5) - 1)/(3(-3((1(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1))/(3(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1) + 3)) + 5) + 1)) - 2)/(3((-1(-3((1(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1))/(3(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1) + 3)) + 5) - 1)/(3(-3((1(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1))/(3(1cos(1\u03c0((1x + 3)/(1x)) + 3) + 1) + 3)) + 5) + 1)) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-3|(2sin(1\u03c0(-1|(-2((2x - 2)/(-1x + 2))^2 + 1((2x - 2)/(-1x + 2)) - 3) - 3| + 1) - 3) - 1) + 1|)^2 - 1(-3|(2sin(1\u03c0(-1|(-2((2x - 2)/(-1x + 2))^2 + 1((2x - 2)/(-1x + 2)) - 3) - 3| + 1) - 3) - 1) + 1|) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(-3|((1(-1|(4(-2x^2 + 5) - 2) - 2| + 2) + 2)/(1(-1|(4(-2x^2 + 5) - 2) - 2| + 2) - 3)) + 1| + 3) + 1| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|((-1(3|(-2(3|(1x - 1) - 1| - 2) - 4) + 3| - 3))/(3(3|(-2(3|(1x - 1) - 1| - 2) - 4) + 3| - 3) + 2)) - 1| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3|(1|(-1cos(1\u03c0(5(3x - 1)^2 - 1) - 3) - 3) - 3| - 1) - 2| + 3)| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(-2sin(2\u03c0(1|(1|(-3|(2x^2 + 1x - 5) - 1| - 3)| + 2) - 2| - 2) - 2) - 1)^2 - 4(-2sin(2\u03c0(1|(1|(-3|(2x^2 + 1x - 5) - 1| - 3)| + 2) - 2| - 2) - 2) - 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-4(4(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3)^2 - 1(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3) + 4)^2 + 5(4(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3)^2 - 1(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3) + 4) + 3) + 1)/(2(-4(4(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3)^2 - 1(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3) + 4)^2 + 5(4(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3)^2 - 1(-1cos(2\u03c0(-2|(-2|x - 1| + 1)| + 3) - 1) + 3) + 4) + 3) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-1(-1|(-1|(-2cos(1\u03c0(1|x + 2| + 2) - 1) - 3)| + 1) - 2| + 2) - 4) + 1)/(1(-1(-1|(-1|(-2cos(1\u03c0(1|x + 2| + 2) - 1) - 3)| + 1) - 2| + 2) - 4) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(-1|(2(-2(-1(-2|x + 2| + 1)^2 - 5(-2|x + 2| + 1) + 1)) - 3)|) - 2)/(1(-1|(2(-2(-1(-2|x + 2| + 1)^2 - 5(-2|x + 2| + 1) + 1)) - 3)|) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((3(1(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1)^2 + 5(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1) - 4) - 1)/(-2(1(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1)^2 + 5(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1) - 4) - 2))^2 - 5((3(1(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1)^2 + 5(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1) - 4) - 1)/(-2(1(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1)^2 + 5(1(-2|(2x^2 - 3x - 3) + 2| + 2) - 1) - 4) - 2)) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(3cos(3\u03c0(-1|((2(-2(1x + 4) + 3) - 3)/(-1(-2(1x + 4) + 3) - 3)) + 1| - 2)) + 2) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(1|((-3(-2|(-2(-3x^2 + 3x + 4)^2 - 5(-3x^2 + 3x + 4) + 5) - 1| - 1) - 1)/(-2(-2|(-2(-3x^2 + 3x + 4)^2 - 5(-3x^2 + 3x + 4) + 5) - 1| - 1) - 3)) + 1| - 3)^2 - 5(1|((-3(-2|(-2(-3x^2 + 3x + 4)^2 - 5(-3x^2 + 3x + 4) + 5) - 1| - 1) - 1)/(-2(-2|(-2(-3x^2 + 3x + 4)^2 - 5(-3x^2 + 3x + 4) + 5) - 1| - 1) - 3)) + 1| - 3) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(-2|(-1|(3(1|(2|x + 1| - 1)| - 1)^2 + 2(1|(2|x + 1| - 1)| - 1) - 5)|) + 2| - 3) - 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(-2(-2sin(3\u03c0(2(2|(2|x| + 3) + 2| - 2) + 2) + 1) - 3) - 2) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(1(-1(-3(-2(-2|x + 1|) - 2)^2 + 3(-2(-2|x + 1|) - 2) + 2)^2 + 5(-3(-2(-2|x + 1|) - 2)^2 + 3(-2(-2|x + 1|) - 2) + 2) - 3)^2 + 1) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(3|(-1|(-1|(-3sin(1\u03c0(-4x + 2)) + 1)| - 2) + 1|) - 1| + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(3sin(2\u03c0(-1|(3(-2|(4x^2 + 1x + 3) + 2| - 1) + 3) - 2| + 1) + 2) - 2) + 2| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1e^(-1(-1((-3(-5(-1|((1x + 1)/(-2x + 3)) + 2| + 2)^2 + 4(-1|((1x + 1)/(-2x + 3)) + 2| + 2) + 4))/(-3(-5(-1|((1x + 1)/(-2x + 3)) + 2| + 2)^2 + 4(-1|((1x + 1)/(-2x + 3)) + 2| + 2) + 4) + 4))^2 + 1((-3(-5(-1|((1x + 1)/(-2x + 3)) + 2| + 2)^2 + 4(-1|((1x + 1)/(-2x + 3)) + 2| + 2) + 4))/(-3(-5(-1|((1x + 1)/(-2x + 3)) + 2| + 2)^2 + 4(-1|((1x + 1)/(-2x + 3)) + 2| + 2) + 4) + 4)) - 1)) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(2cos(1\u03c0(-5(-1|(3((2x + 1)/(1x - 3))^2 - 4((2x + 1)/(1x - 3)) + 3) + 2| - 3) - 3) + 2) - 2))/(-2(2cos(1\u03c0(-5(-1|(3((2x + 1)/(1x - 3))^2 - 4((2x + 1)/(1x - 3)) + 3) + 2| - 3) - 3) + 2) - 2) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(-2|(-1cos(2\u03c0(4(-5(-2|x - 2|)) - 5) - 2) - 1) + 1| + 3) + 2|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-3|(-1|(3sin(3\u03c0((-2(3|x + 1| - 3) + 2)/(2(3|x + 1| - 3) - 1)) + 1)) + 2|) - 2|) + 3| + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2sin(2\u03c0(-1|(-1|(-1|((-3((-2x + 1)/(-1x - 1)) - 1)/(-2((-2x + 1)/(-1x - 1)) - 2)) - 2| - 2) + 3| - 1) + 1| - 2) + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(-2(-3|(-5(2|(1x + 4) + 2| - 3)^2 + 2) - 1|) - 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-1(3sin(3\u03c0(3(3(1x + 1) + 1)) + 3) + 2) - 2) - 3)/(-1(-1(3sin(3\u03c0(3(3(1x + 1) + 1)) + 3) + 2) - 2) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(-1cos(3\u03c0(-1(-2(-5((3x - 3)/(1x))^2 + 5((3x - 3)/(1x)) - 4) + 5)^2 + 2(-2(-5((3x - 3)/(1x))^2 + 5((3x - 3)/(1x)) - 4) + 5) + 5) - 2) + 1))/(-2(-1cos(3\u03c0(-1(-2(-5((3x - 3)/(1x))^2 + 5((3x - 3)/(1x)) - 4) + 5)^2 + 2(-2(-5((3x - 3)/(1x))^2 + 5((3x - 3)/(1x)) - 4) + 5) + 5) - 2) + 1) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(2|(1(2|(-1(-3|x + 2| + 2) - 2) + 3| + 1)^2 - 5(2|(-1(-3|x + 2| + 2) - 2) + 3| + 1) - 1) + 2|))/(-1(2|(1(2|(-1(-3|x + 2| + 2) - 2) + 3| + 1)^2 - 5(2|(-1(-3|x + 2| + 2) - 2) + 3| + 1) - 1) + 2|) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(2\u03c0(-2(1(-3(3((1x - 2)/(1x)) - 1) - 3)^2 + 5(-3(3((1x - 2)/(1x)) - 1) - 3) + 1) - 4) - 2) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(4(4(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2)^2 + 2(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2) + 4)^2 - 2(4(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2)^2 + 2(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2) + 4) - 1) + 3)/(1(4(4(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2)^2 + 2(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2) + 4)^2 - 2(4(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2)^2 + 2(2sin(1\u03c0(1|(5x^2 - 2x - 1) - 2| - 1) + 3) + 2) + 4) - 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(2cos(3\u03c0(5((2((-2(2|x + 1| - 1))/(2(2|x + 1| - 1) + 1)) + 3)/(2((-2(2|x + 1| - 1))/(2(2|x + 1| - 1) + 1)))) - 1) + 3) - 2) - 2| - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4((-1(4((2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 3)/(-2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 1))^2 + 1((2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 3)/(-2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 1)) - 4) + 3)/(1(4((2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 3)/(-2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 1))^2 + 1((2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 3)/(-2(-3sin(1\u03c0((3x - 3)/(3x)) + 2)) + 1)) - 4))) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(3((-1((1(5(3sin(1\u03c0x + 1) + 3) + 2) - 2)/(2(5(3sin(1\u03c0x + 1) + 3) + 2))) - 2)/(-2((1(5(3sin(1\u03c0x + 1) + 3) + 2) - 2)/(2(5(3sin(1\u03c0x + 1) + 3) + 2))) + 3))^2 - 1((-1((1(5(3sin(1\u03c0x + 1) + 3) + 2) - 2)/(2(5(3sin(1\u03c0x + 1) + 3) + 2))) - 2)/(-2((1(5(3sin(1\u03c0x + 1) + 3) + 2) - 2)/(2(5(3sin(1\u03c0x + 1) + 3) + 2))) + 3)) - 3) - 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((-1(-1cos(2\u03c0(1(-4(-5x^2 + 2) - 3)^2 + 1) + 3) + 2) - 3)/(2(-1cos(2\u03c0(1(-4(-5x^2 + 2) - 3)^2 + 1) + 3) + 2)))^2 + 1((-1(-1cos(2\u03c0(1(-4(-5x^2 + 2) - 3)^2 + 1) + 3) + 2) - 3)/(2(-1cos(2\u03c0(1(-4(-5x^2 + 2) - 3)^2 + 1) + 3) + 2))) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4((2(-1((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))^2 - 3((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))) - 3)/(2(-1((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))^2 - 3((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))) + 2))^2 - 5((2(-1((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))^2 - 3((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))) - 3)/(2(-1((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))^2 - 3((-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4) - 3)/(-1(5(3sin(3\u03c0x + 2) + 1)^2 - 5(3sin(3\u03c0x + 2) + 1) - 4)))) + 2)) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3((3(-3sin(3\u03c0(4((1(-2x + 1) + 3)/(-3(-2x + 1) + 4)) + 4) + 3) - 2) + 1)/(1(-3sin(3\u03c0(4((1(-2x + 1) + 3)/(-3(-2x + 1) + 4)) + 4) + 3) - 2) + 1))^2 - 2((3(-3sin(3\u03c0(4((1(-2x + 1) + 3)/(-3(-2x + 1) + 4)) + 4) + 3) - 2) + 1)/(1(-3sin(3\u03c0(4((1(-2x + 1) + 3)/(-3(-2x + 1) + 4)) + 4) + 3) - 2) + 1)) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-2(3(1sin(2\u03c0(1(2|x|)^2 + 2(2|x|) + 2)))) - 3) + 3| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((-1(1sin(3\u03c0(-2(1|(-1x + 2) - 2| - 1)^2 - 3(1|(-1x + 2) - 2| - 1) + 1) - 1)) + 2)/(-2(1sin(3\u03c0(-2(1|(-1x + 2) - 2| - 1)^2 - 3(1|(-1x + 2) - 2| - 1) + 1) - 1)) - 3))^2 - 2((-1(1sin(3\u03c0(-2(1|(-1x + 2) - 2| - 1)^2 - 3(1|(-1x + 2) - 2| - 1) + 1) - 1)) + 2)/(-2(1sin(3\u03c0(-2(1|(-1x + 2) - 2| - 1)^2 - 3(1|(-1x + 2) - 2| - 1) + 1) - 1)) - 3)) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(3|(-2(2(-1cos(2\u03c0((2x - 3)/(1x)) + 3) - 1)^2 - 4)^2 - 4(2(-1cos(2\u03c0((2x - 3)/(1x)) + 3) - 1)^2 - 4) + 3) + 2| + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((1(3cos(1\u03c0(-1(1((-1x - 2)/(-2x + 3))^2 - 2((-1x - 2)/(-2x + 3)) - 4) + 4) + 1) + 2))/(1(3cos(1\u03c0(-1(1((-1x - 2)/(-2x + 3))^2 - 2((-1x - 2)/(-2x + 3)) - 4) + 4) + 1) + 2) - 3)) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(-1(2sin(1\u03c0(-1|(-2|(1x + 5) + 1| + 2) - 1| - 3) + 1) + 1)^2 - 1(2sin(1\u03c0(-1|(-2|(1x + 5) + 1| + 2) - 1| - 3) + 1) + 1) + 3) - 2)/(-3(-1(2sin(1\u03c0(-1|(-2|(1x + 5) + 1| + 2) - 1| - 3) + 1) + 1)^2 - 1(2sin(1\u03c0(-1|(-2|(1x + 5) + 1| + 2) - 1| - 3) + 1) + 1) + 3) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(2(-1|(1|(2|(3x^2 - 4x - 3)| + 2) - 1| - 3) - 2| + 2)^2 + 2(-1|(1|(2|(3x^2 - 4x - 3)| + 2) - 1| - 3) - 2| + 2) + 5) - 2| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(2((2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3))/(-2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3) - 3))^2 - 3((2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3))/(-2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3) - 3)) - 1) + 1)/(2(2((2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3))/(-2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3) - 3))^2 - 3((2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3))/(-2(3((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3))^2 - 1((1(1cos(1\u03c0x + 1) + 3) + 3)/(-2(1cos(1\u03c0x + 1) + 3) + 3)) + 3) - 3)) - 1) - 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(-3|(-2cos(2\u03c0(-2|(-1|((3x - 1)/(-1x - 1)) + 3| + 3) + 2| + 3) - 1) + 1)| + 3) - 1)/(2(-3|(-2cos(2\u03c0(-2|(-1|((3x - 1)/(-1x - 1)) + 3| + 3) + 2| + 3) - 1) + 1)| + 3) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(-2(-2|(5((1(-3cos(2\u03c0x + 2)))/(3(-3cos(2\u03c0x + 2)) + 3))^2 + 5((1(-3cos(2\u03c0x + 2)))/(3(-3cos(2\u03c0x + 2)) + 3)) + 2) - 3| + 3) - 1) + 1| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(2(-2sin(3\u03c0((3(4(-1|x - 1| + 2) - 4) - 2)/(1(4(-1|x - 1| + 2) - 4) + 3)) - 1) + 3) - 5) + 1)/(1(2(-2sin(3\u03c0((3(4(-1|x - 1| + 2) - 4) - 2)/(1(4(-1|x - 1| + 2) - 4) + 3)) - 1) + 3) - 5) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1cos(2\u03c0(-3((-1((2(2|(-2x + 4) - 2| - 2) - 2)/(3(2|(-2x + 4) - 2| - 2) + 3)) - 1)/(1((2(2|(-2x + 4) - 2| - 2) - 2)/(3(2|(-2x + 4) - 2| - 2) + 3)) - 2)) + 3) + 2) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-1|(-5(-1|(2cos(3\u03c0(2|x + 1| - 1) - 3) + 3) - 2| + 2) + 4) + 3| - 1)^2 + 5(-1|(-5(-1|(2cos(3\u03c0(2|x + 1| - 1) - 3) + 3) - 2| + 2) + 4) + 3| - 1) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(-1((-1(1sin(3\u03c0(3(-2|x| + 3)^2 - 2(-2|x| + 3) + 1) - 3) - 2) - 1)/(-3(1sin(3\u03c0(3(-2|x| + 3)^2 - 2(-2|x| + 3) + 1) - 3) - 2) - 1))^2 + 3((-1(1sin(3\u03c0(3(-2|x| + 3)^2 - 2(-2|x| + 3) + 1) - 3) - 2) - 1)/(-3(1sin(3\u03c0(3(-2|x| + 3)^2 - 2(-2|x| + 3) + 1) - 3) - 2) - 1)) + 2) - 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1(1(-4(-1cos(1\u03c0(2x + 1) - 1) - 1) - 5) + 4)^2 + 5(1(-4(-1cos(1\u03c0(2x + 1) - 1) - 1) - 5) + 4) - 5) - 2)/(3(-1(1(-4(-1cos(1\u03c0(2x + 1) - 1) - 1) - 5) + 4)^2 + 5(1(-4(-1cos(1\u03c0(2x + 1) - 1) - 1) - 5) + 4) - 5) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(4(-3sin(1\u03c0(-1(4(-3x - 5) - 3) + 5) + 2) + 2) - 1)^2 - 2(4(-3sin(1\u03c0(-1(4(-3x - 5) - 3) + 5) + 2) + 2) - 1) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(2|(2|(3sin(3\u03c0((1(-1x^2 - 2x - 3) + 3)/(-1(-1x^2 - 2x - 3) + 2)) - 1) - 3) - 1| + 1) - 2| + 1)^2 + 5(2|(2|(3sin(3\u03c0((1(-1x^2 - 2x - 3) + 3)/(-1(-1x^2 - 2x - 3) + 2)) - 1) - 3) - 1| + 1) - 2| + 1) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-1(2(1cos(2\u03c0(-3((3x + 3)/(-1x + 2)) - 5) - 1) - 2)^2 - 1(1cos(2\u03c0(-3((3x + 3)/(-1x + 2)) - 5) - 1) - 2) + 4)^2) + 1)/(-2(-1(2(1cos(2\u03c0(-3((3x + 3)/(-1x + 2)) - 5) - 1) - 2)^2 - 1(1cos(2\u03c0(-3((3x + 3)/(-1x + 2)) - 5) - 1) - 2) + 4)^2) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3(-2|(1|(-2|(-1x + 4) + 1|) + 3| + 3) - 3|)^2 + 3(-2|(1|(-2|(-1x + 4) + 1|) + 3| + 3) - 3|) + 3) + 3| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(2|(2|((-1(-3sin(2\u03c0((-1x + 3)/(-3x + 1)) + 1) + 3) - 1)/(-2(-3sin(2\u03c0((-1x + 3)/(-3x + 1)) + 1) + 3) - 1))| + 3) - 3| - 3)^2 - 1(2|(2|((-1(-3sin(2\u03c0((-1x + 3)/(-3x + 1)) + 1) + 3) - 1)/(-2(-3sin(2\u03c0((-1x + 3)/(-3x + 1)) + 1) + 3) - 1))| + 3) - 3| - 3) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1|(2(-2((2(2cos(1\u03c0x + 3) - 1) - 1)/(-2(2cos(1\u03c0x + 3) - 1) - 3))^2 - 4((2(2cos(1\u03c0x + 3) - 1) - 1)/(-2(2cos(1\u03c0x + 3) - 1) - 3))) + 4)| - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(3cos(2\u03c0(-3(-4((3((-1x - 1)/(-3x + 2)) + 1)/(-2((-1x - 1)/(-3x + 2)) + 3))^2 + 4((3((-1x - 1)/(-3x + 2)) + 1)/(-2((-1x - 1)/(-3x + 2)) + 3)) - 3)^2 + 2(-4((3((-1x - 1)/(-3x + 2)) + 1)/(-2((-1x - 1)/(-3x + 2)) + 3))^2 + 4((3((-1x - 1)/(-3x + 2)) + 1)/(-2((-1x - 1)/(-3x + 2)) + 3)) - 3) - 4)) - 2) + 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (3(-4(1sin(1\u03c0((3(-2|(-1|x - 3| + 2) + 3| - 1) + 3)/(2(-2|(-1|x - 3| + 2) + 3| - 1))) + 3)) + 3) + 2)/(3(-4(1sin(1\u03c0((3(-2|(-1|x - 3| + 2) + 3| - 1) + 3)/(2(-2|(-1|x - 3| + 2) + 3| - 1))) + 3)) + 3) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1((1(-4(-1|(-2sin(3\u03c0(-1|x - 3|) + 1)) + 2| + 2)^2 + 3(-1|(-2sin(3\u03c0(-1|x - 3|) + 1)) + 2| + 2) - 1) + 3)/(-2(-4(-1|(-2sin(3\u03c0(-1|x - 3|) + 1)) + 2| + 2)^2 + 3(-1|(-2sin(3\u03c0(-1|x - 3|) + 1)) + 2| + 2) - 1) - 2)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-5(3cos(2\u03c0(1(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1)^2 - 5(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1) - 5) - 2) + 2)^2 - 1(3cos(2\u03c0(1(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1)^2 - 5(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1) - 5) - 2) + 2) + 4) + 3)/(2(-5(3cos(2\u03c0(1(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1)^2 - 5(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1) - 5) - 2) + 2)^2 - 1(3cos(2\u03c0(1(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1)^2 - 5(-5((-3x + 1)/(3x - 2))^2 + 5((-3x + 1)/(3x - 2)) - 1) - 5) - 2) + 2) + 4) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-1((2((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)))/(3((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)) + 1))^2 - 1((2((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)))/(3((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)) + 1))) + 2)/(-1(-1((2((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)))/(3((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)) + 1))^2 - 1((2((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)))/(3((-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 1)/(-1(5(-1sin(2\u03c0x + 3) + 3)^2 - 1(-1sin(2\u03c0x + 3) + 3) + 3) + 3)) + 1))) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2sin(2\u03c0(-3(-3(-5((1(-3|x - 1| + 1) + 1)/(2(-3|x - 1| + 1) - 1)) + 4)^2 + 5(-5((1(-3|x - 1| + 1) + 1)/(2(-3|x - 1| + 1) - 1)) + 4) - 3)^2 - 5(-3(-5((1(-3|x - 1| + 1) + 1)/(2(-3|x - 1| + 1) - 1)) + 4)^2 + 5(-5((1(-3|x - 1| + 1) + 1)/(2(-3|x - 1| + 1) - 1)) + 4) - 3) - 3) - 3) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1((-3(-1(-2cos(1\u03c0(-1(2|x - 3| + 1) - 4) - 2) - 1) - 5) - 2)/(-1(-1(-2cos(1\u03c0(-1(2|x - 3| + 1) - 4) - 2) - 1) - 5) - 2)) + 2)/(-2((-3(-1(-2cos(1\u03c0(-1(2|x - 3| + 1) - 4) - 2) - 1) - 5) - 2)/(-1(-1(-2cos(1\u03c0(-1(2|x - 3| + 1) - 4) - 2) - 1) - 5) - 2))), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(3|((-1(3cos(3\u03c0(-3|((1x + 3)/(-1x - 1)) + 2|) - 1) + 3) - 3)/(-1(3cos(3\u03c0(-3|((1x + 3)/(-1x - 1)) + 2|) - 1) + 3) + 2)) + 2| + 2)| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1sin(1\u03c0(-4(3|((-2(-1(-1x - 4)^2 + 3(-1x - 4) - 1))/(2(-1(-1x - 4)^2 + 3(-1x - 4) - 1) + 3))| - 1) + 1) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(3(-3|(-4(1|(2|x| - 3) + 2|)^2 + 5(1|(2|x| - 3) + 2|) - 4)| + 3)^2 + 4) - 1)/(-2(3(-3|(-4(1|(2|x| - 3) + 2|)^2 + 5(1|(2|x| - 3) + 2|) - 4)| + 3)^2 + 4) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(1((-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2) + 2)/(-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2)))^2 - 2((-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2) + 2)/(-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2))) - 5) - 2)/(-2(1((-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2) + 2)/(-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2)))^2 - 2((-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2) + 2)/(-1(1sin(1\u03c0(-2|(-5x^2 + 5x + 5) - 1|)) + 2))) - 5) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((1(1((1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2) + 2)/(-1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2)))^2 - 4((1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2) + 2)/(-1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2))) + 4) + 1)/(-2(1((1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2) + 2)/(-1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2)))^2 - 4((1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2) + 2)/(-1(2cos(1\u03c0(2|x + 2| - 2) - 2) - 2))) + 4) - 3)) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3|(2((-1((-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 2)/(-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 3)) - 1)/(-1((-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 2)/(-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 3)) - 2))^2 - 5((-1((-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 2)/(-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 3)) - 1)/(-1((-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 2)/(-1(-3|(2sin(3\u03c0x + 3) - 2) - 3| - 1) + 3)) - 2)) - 5) + 1| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(1(2|(1sin(2\u03c0(1((2x + 2)/(2x + 3)) + 4)) - 3) - 2| + 2) - 2) + 2| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5(-3(-2(-1cos(3\u03c0(2((1x + 2)/(-3x + 1)) - 3) - 1) - 2) - 5) - 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2sin(1\u03c0(1|(-1(-2((3(-4x + 3) - 2)/(2(-4x + 3)))^2 + 2((3(-4x + 3) - 2)/(2(-4x + 3))) + 5)^2 - 4(-2((3(-4x + 3) - 2)/(2(-4x + 3)))^2 + 2((3(-4x + 3) - 2)/(2(-4x + 3))) + 5) + 4)| + 2) - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(4(3sin(2\u03c0(3((3(-1|x - 2| + 1) + 3)/(-2(-1|x - 2| + 1) - 3))^2 + 2((3(-1|x - 2| + 1) + 3)/(-2(-1|x - 2| + 1) - 3)) + 3) + 1) - 3) - 4) - 1| - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(1|(-1(-1|(-2(3x^2 - 2x - 5) - 4) - 1| + 2)^2 - 5(-1|(-2(3x^2 - 2x - 5) - 4) - 1| + 2) + 4) + 2|) + 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|((2(-2cos(2\u03c0(3|((3((-1x + 1)/(-2x + 3)) - 3)/(2((-1x + 1)/(-2x + 3)) - 1)) + 2|) - 1) - 1) + 3)/(1(-2cos(2\u03c0(3|((3((-1x + 1)/(-2x + 3)) - 3)/(2((-1x + 1)/(-2x + 3)) - 1)) + 2|) - 1) - 1) + 3)) + 1| + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((1((1(2|(-2|(3cos(2\u03c0x)) + 2| + 1) - 2|) - 2)/(1(2|(-2|(3cos(2\u03c0x)) + 2| + 1) - 2|) - 3)) - 3)/(-1((1(2|(-2|(3cos(2\u03c0x)) + 2| + 1) - 2|) - 2)/(1(2|(-2|(3cos(2\u03c0x)) + 2| + 1) - 2|) - 3)) + 2)) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|((-2(-1|(-4(-2|((-1x)/(2x - 1)) - 1| + 2)^2 + 2(-2|((-1x)/(2x - 1)) - 1| + 2) + 1) - 1| - 3))/(-3(-1|(-4(-2|((-1x)/(2x - 1)) - 1| + 2)^2 + 2(-2|((-1x)/(2x - 1)) - 1| + 2) + 1) - 1| - 3) - 1)) - 2| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(1|((3(5(-3(2sin(2\u03c0x - 2) + 3)^2 - 4(2sin(2\u03c0x - 2) + 3) + 2)^2 + 2(-3(2sin(2\u03c0x - 2) + 3)^2 - 4(2sin(2\u03c0x - 2) + 3) + 2) + 3) - 1)/(-1(5(-3(2sin(2\u03c0x - 2) + 3)^2 - 4(2sin(2\u03c0x - 2) + 3) + 2)^2 + 2(-3(2sin(2\u03c0x - 2) + 3)^2 - 4(2sin(2\u03c0x - 2) + 3) + 2) + 3) - 1))| + 2)| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-4(-1(-3(3|(1x - 1) - 2| - 2)^2 + 2(3|(1x - 1) - 2| - 2)) - 4)) + 2| negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|((1(3(-2cos(2\u03c0(4((2x)/(2x - 1))^2 - 2((2x)/(2x - 1)) - 3) - 1) - 1)^2 - 2(-2cos(2\u03c0(4((2x)/(2x - 1))^2 - 2((2x)/(2x - 1)) - 3) - 1) - 1) + 3) - 2)/(2(3(-2cos(2\u03c0(4((2x)/(2x - 1))^2 - 2((2x)/(2x - 1)) - 3) - 1) - 1)^2 - 2(-2cos(2\u03c0(4((2x)/(2x - 1))^2 - 2((2x)/(2x - 1)) - 3) - 1) - 1) + 3) + 3)) + 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3sin(2\u03c0(4((3(3(-2|(2|x - 3| - 3) - 1| + 2) + 1) - 1)/(-1(3(-2|(2|x - 3| - 3) - 1| + 2) + 1) + 2)) + 4) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(3|(5((-2(5(-1|x + 1| + 2)^2 - 5(-1|x + 1| + 2) - 4) - 3)/(2(5(-1|x + 1| + 2)^2 - 5(-1|x + 1| + 2) - 4) + 1)) + 4) + 3| - 1) + 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5((-2(-1(1(3cos(1\u03c0(-3x^2 + 1x - 3) - 1) - 3) - 2) + 3))/(-2(-1(1(3cos(1\u03c0(-3x^2 + 1x - 3) - 1) - 3) - 2) + 3) + 3)) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-2|((-1(1(-5(3cos(1\u03c0x - 2) + 1) + 4)^2 - 4(-5(3cos(1\u03c0x - 2) + 1) + 4) + 3) + 2)/(-2(1(-5(3cos(1\u03c0x - 2) + 1) + 4)^2 - 4(-5(3cos(1\u03c0x - 2) + 1) + 4) + 3) - 3)) - 1|) + 3)/(-3(-2|((-1(1(-5(3cos(1\u03c0x - 2) + 1) + 4)^2 - 4(-5(3cos(1\u03c0x - 2) + 1) + 4) + 3) + 2)/(-2(1(-5(3cos(1\u03c0x - 2) + 1) + 4)^2 - 4(-5(3cos(1\u03c0x - 2) + 1) + 4) + 3) - 3)) - 1|) + 4) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(2|(-2(3cos(3\u03c0(3(-5x + 4) - 5) + 1) + 3)^2 - 1(3cos(3\u03c0(3(-5x + 4) - 5) + 1) + 3) - 5) - 1| + 3) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3((1(-4(3cos(2\u03c0((-3((1x - 3)/(-1x)) - 3)/(2((1x - 3)/(-1x)) - 1)) - 1) + 3) - 5) + 3)/(1(-4(3cos(2\u03c0((-3((1x - 3)/(-1x)) - 3)/(2((1x - 3)/(-1x)) - 1)) - 1) + 3) - 5) + 2)) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1sin(1\u03c0(1((3(3|(2(3x^2 + 5x - 5)^2 - 3(3x^2 + 5x - 5) - 5) - 3|) + 1)/(3(3|(2(3x^2 + 5x - 5)^2 - 3(3x^2 + 5x - 5) - 5) - 3|) - 1))^2 + 3) - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(1((-3(-5(-1sin(1\u03c0(3x - 1) - 1) + 3)^2 - 5(-1sin(1\u03c0(3x - 1) - 1) + 3) - 3) - 1)/(2(-5(-1sin(1\u03c0(3x - 1) - 1) + 3)^2 - 5(-1sin(1\u03c0(3x - 1) - 1) + 3) - 3) + 2))^2 - 2((-3(-5(-1sin(1\u03c0(3x - 1) - 1) + 3)^2 - 5(-1sin(1\u03c0(3x - 1) - 1) + 3) - 3) - 1)/(2(-5(-1sin(1\u03c0(3x - 1) - 1) + 3)^2 - 5(-1sin(1\u03c0(3x - 1) - 1) + 3) - 3) + 2)) + 3) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(1|(2sin(3\u03c0(1(1|(2|x + 1|) + 3| - 2)^2 + 2(1|(2|x + 1|) + 3| - 2) + 5) + 2) - 1) + 3|) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(2(-3|(-2((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1))^2 - 1((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1)) - 1) + 1|)^2 + 4(-3|(-2((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1))^2 - 1((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1)) - 1) + 1|) + 1)^2 - 2(2(-3|(-2((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1))^2 - 1((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1)) - 1) + 1|)^2 + 4(-3|(-2((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1))^2 - 1((1(-4x^2 - 3x - 1) + 1)/(2(-4x^2 - 3x - 1) - 1)) - 1) + 1|) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-2(-3sin(3\u03c0(-1((3(-4x - 3) - 2)/(1(-4x - 3) + 2))^2 + 5((3(-4x - 3) - 2)/(1(-4x - 3) + 2)) + 2) - 3) - 3)^2 + 2) - 1)/(-2(-2(-3sin(3\u03c0(-1((3(-4x - 3) - 2)/(1(-4x - 3) + 2))^2 + 5((3(-4x - 3) - 2)/(1(-4x - 3) + 2)) + 2) - 3) - 3)^2 + 2) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((1(5(-1(1|(-3cos(1\u03c0x + 3) - 2) - 2| - 1) + 5) + 4) + 2)/(3(5(-1(1|(-3cos(1\u03c0x + 3) - 2) - 2| - 1) + 5) + 4) + 2)) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2((1((-2(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)/(-1(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)) + 2)/(3((-2(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)/(-1(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)) - 2)) - 3)/(-2((1((-2(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)/(-1(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)) + 2)/(3((-2(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)/(-1(2sin(2\u03c0(3|(4x^2 + 5x - 2)| - 3) - 2)) - 2)) - 2)) + 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(1sin(1\u03c0(-2(-1(2((-3x + 2)/(-1x + 2)) + 5) - 3) + 1)) + 2) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2cos(3\u03c0(1|(-1(3|(-3((1x)/(3x - 2))^2 - 5((1x)/(3x - 2)) - 1)| - 1))|)) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(2cos(2\u03c0(2|((2((3((-2x - 1)/(3x)) + 2)/(1((-2x - 1)/(3x)) + 3)) - 2)/(2((3((-2x - 1)/(3x)) + 2)/(1((-2x - 1)/(3x)) + 3))))| + 2) + 1) - 3)^2 - 3(2cos(2\u03c0(2|((2((3((-2x - 1)/(3x)) + 2)/(1((-2x - 1)/(3x)) + 3)) - 2)/(2((3((-2x - 1)/(3x)) + 2)/(1((-2x - 1)/(3x)) + 3))))| + 2) + 1) - 3) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2(2|(-3|((-2(3|(1|x - 3| - 2)| + 1) - 3)/(-2(3|(1|x - 3| - 2)| + 1) + 1)) - 2| - 3) - 2| - 2)^2 + 3(2|(-3|((-2(3|(1|x - 3| - 2)| + 1) - 3)/(-2(3|(1|x - 3| - 2)| + 1) + 1)) - 2| - 3) - 2| - 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-3(3|(-2sin(2\u03c0(-1|(-3x^2 - 2x - 2) - 1| - 2) + 3) + 3) + 3|) + 2) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(3|(2(-2|(2|(-4x^2 - 5x + 3) - 3| + 2) - 3| - 3)^2 - 2(-2|(2|(-4x^2 - 5x + 3) - 3| + 2) - 3| - 3) - 1) - 1| + 2))/(-2(3|(2(-2|(2|(-4x^2 - 5x + 3) - 3| + 2) - 3| - 3)^2 - 2(-2|(2|(-4x^2 - 5x + 3) - 3| + 2) - 3| - 3) - 1) - 1| + 2) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-3|(1(2|(1|(-1|x + 3| + 2) - 2| - 3) - 3| - 2)^2 - 1(2|(1|(-1|x + 3| + 2) - 2| - 3) - 3| - 2) - 3) - 2| - 1) - 2)/(3(-3|(1(2|(1|(-1|x + 3| + 2) - 2| - 3) - 3| - 2)^2 - 1(2|(1|(-1|x + 3| + 2) - 2| - 3) - 3| - 2) - 3) - 2| - 1) + 1) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(1|(2|(-2|(3(-2cos(3\u03c0x - 1)) + 1) - 3| + 2) - 3| + 3)| - 2) + 2| + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1(1sin(2\u03c0(1(-1(-2x^2 - 3x + 2)^2 - 5(-2x^2 - 3x + 2) - 3)^2) + 1) - 2)) + 3| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(3(-3|(-1sin(3\u03c0(3|(-5x + 5) + 3| + 1) - 2) + 3) + 1| - 2) + 1) - 2)/(-2(3(-3|(-1sin(3\u03c0(3|(-5x + 5) + 3| + 1) - 2) + 3) + 1| - 2) + 1) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((3(-1(2|(1sin(1\u03c0(4x^2 - 2x + 5) - 1) + 1) - 2|) + 2) + 3)/(1(-1(2|(1sin(1\u03c0(4x^2 - 2x + 5) - 1) + 1) - 2|) + 2) - 2))^2 + 4((3(-1(2|(1sin(1\u03c0(4x^2 - 2x + 5) - 1) + 1) - 2|) + 2) + 3)/(1(-1(2|(1sin(1\u03c0(4x^2 - 2x + 5) - 1) + 1) - 2|) + 2) - 2)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(2sin(2\u03c0(-1(-3(-1|(1x^2 - 4x - 1)|)^2 - 5(-1|(1x^2 - 4x - 1)|) - 1)^2 - 2(-3(-1|(1x^2 - 4x - 1)|)^2 - 5(-1|(1x^2 - 4x - 1)|) - 1) + 2) + 1) + 3) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5((-1(-2sin(2\u03c0(2(1|(-1x + 4) + 1|) - 1) - 2) + 3) + 1)/(1(-2sin(2\u03c0(2(1|(-1x + 4) + 1|) - 1) - 2) + 3)))^2 + 5((-1(-2sin(2\u03c0(2(1|(-1x + 4) + 1|) - 1) - 2) + 3) + 1)/(1(-2sin(2\u03c0(2(1|(-1x + 4) + 1|) - 1) - 2) + 3))) + 5 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(1(3(1(-4(-2sin(2\u03c0x + 2) - 1)^2 + 2(-2sin(2\u03c0x + 2) - 1) + 1) + 4) - 2) - 1) + 1)/(-1(1(3(1(-4(-2sin(2\u03c0x + 2) - 1)^2 + 2(-2sin(2\u03c0x + 2) - 1) + 1) + 4) - 2) - 1) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(2|(-2((1(3|(-3x^2 + 5x + 2) - 3|) + 3)/(-3(3|(-3x^2 + 5x + 2) - 3|) - 1))^2 + 5((1(3|(-3x^2 + 5x + 2) - 3|) + 3)/(-3(3|(-3x^2 + 5x + 2) - 3|) - 1)) + 3)| - 1) - 2| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3e^(-2((-2(-2(-2|(-2(-2|x - 1| + 1)^2 - 5(-2|x - 1| + 1) + 4) + 2| - 3) - 2) - 1)/(2(-2(-2|(-2(-2|x - 1| + 1)^2 - 5(-2|x - 1| + 1) + 4) + 2| - 3) - 2) - 1))) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(3|((1(-1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2)^2 - 1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2) + 2))/(-1(-1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2)^2 - 1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2) + 2) + 2)) + 1| - 1) - 3)/(3(3|((1(-1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2)^2 - 1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2) + 2))/(-1(-1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2)^2 - 1(-2sin(3\u03c0((-3x - 1)/(-2x + 3)) + 2) + 2) + 2) + 2)) + 1| - 1) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((-2(1sin(3\u03c0(-3((-3(4x - 1) - 1)/(2(4x - 1) + 2))^2 - 4((-3(4x - 1) - 1)/(2(4x - 1) + 2)) + 4) + 1) - 3) - 3)/(3(1sin(3\u03c0(-3((-3(4x - 1) - 1)/(2(4x - 1) + 2))^2 - 4((-3(4x - 1) - 1)/(2(4x - 1) + 2)) + 4) + 1) - 3) + 3)) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-2((3(3|(-1(2sin(2\u03c0x - 1))^2 + 1(2sin(2\u03c0x - 1)) + 4) - 3| + 1) + 2)/(-2(3|(-1(2sin(2\u03c0x - 1))^2 + 1(2sin(2\u03c0x - 1)) + 4) - 3| + 1))) - 2) + 2| - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|((2(5(-2sin(1\u03c0(1|((3x - 3)/(1x + 3)) - 2| - 2) + 3) - 1)^2 - 2(-2sin(1\u03c0(1|((3x - 3)/(1x + 3)) - 2| - 2) + 3) - 1) + 4) + 3)/(2(5(-2sin(1\u03c0(1|((3x - 3)/(1x + 3)) - 2| - 2) + 3) - 1)^2 - 2(-2sin(1\u03c0(1|((3x - 3)/(1x + 3)) - 2| - 2) + 3) - 1) + 4) + 2)) - 2| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(5((-3(-3sin(2\u03c0(-5(-1|x|)^2 - 1(-1|x|) - 1) - 2) - 1) - 1)/(-2(-3sin(2\u03c0(-5(-1|x|)^2 - 1(-1|x|) - 1) - 2) - 1) + 3)) + 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-4((3(3sin(1\u03c0(1|(-1x - 5)|) - 2) - 1) + 1)/(1(3sin(1\u03c0(1|(-1x - 5)|) - 2) - 1) + 1))^2 - 5((3(3sin(1\u03c0(1|(-1x - 5)|) - 2) - 1) + 1)/(1(3sin(1\u03c0(1|(-1x - 5)|) - 2) - 1) + 1)) + 1) + 2| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(3\u03c0(-3|((2(4(-2|(1x^2 + 5x - 5) - 3| + 1) + 5) - 2)/(1(4(-2|(1x^2 + 5x - 5) - 3| + 1) + 5) + 3)) + 1| + 1)) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2((3((3(4(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2))^2 + 1(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2)) - 1))/(-3(4(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2))^2 + 1(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2)) - 1) + 1)) + 3)/(-3((3(4(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2))^2 + 1(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2)) - 1))/(-3(4(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2))^2 + 1(5(1x^2 + 3x + 2)^2 + 1(1x^2 + 3x + 2)) - 1) + 1)) + 2))^2 - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1sin(1\u03c0(-2|(2(-1|((-3(-3x^2 + 1x + 2) - 1)/(-2(-3x^2 + 1x + 2) + 3)) - 2| + 2)^2 - 5(-1|((-3(-3x^2 + 1x + 2) - 1)/(-2(-3x^2 + 1x + 2) + 3)) - 2| + 2) - 4) - 1| + 3) + 2) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(1((-3(-2|((-3(-2x^2 - 1x - 3) + 2)/(2(-2x^2 - 1x - 3) + 3)) + 3|) - 1)/(3(-2|((-3(-2x^2 - 1x - 3) + 2)/(2(-2x^2 - 1x - 3) + 3)) + 3|) + 2)) + 1)^2 + 2(1((-3(-2|((-3(-2x^2 - 1x - 3) + 2)/(2(-2x^2 - 1x - 3) + 3)) + 3|) - 1)/(3(-2|((-3(-2x^2 - 1x - 3) + 2)/(2(-2x^2 - 1x - 3) + 3)) + 3|) + 2)) + 1) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5(-1(1|(-1cos(2\u03c0((-3(1x + 2) - 2)/(-2(1x + 2) - 3)) + 2) - 1) + 2|) + 5)^2 - 4(-1(1|(-1cos(2\u03c0((-3(1x + 2) - 2)/(-2(1x + 2) - 3)) + 2) - 1) + 2|) + 5) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-1(-1(-3cos(3\u03c0(2(1|((-2x + 3)/(2x + 3)) + 2| - 1) - 1)) + 1) - 2) - 1)/(-1(-1(-3cos(3\u03c0(2(1|((-2x + 3)/(2x + 3)) + 2| - 1) - 1)) + 1) - 2) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(5((-3(-1(1(-3cos(3\u03c0x + 2)) - 4)^2 - 3(1(-3cos(3\u03c0x + 2)) - 4) - 3) + 1)/(2(-1(1(-3cos(3\u03c0x + 2)) - 4)^2 - 3(1(-3cos(3\u03c0x + 2)) - 4) - 3) + 2))^2 - 1((-3(-1(1(-3cos(3\u03c0x + 2)) - 4)^2 - 3(1(-3cos(3\u03c0x + 2)) - 4) - 3) + 1)/(2(-1(1(-3cos(3\u03c0x + 2)) - 4)^2 - 3(1(-3cos(3\u03c0x + 2)) - 4) - 3) + 2)) + 3) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(3(-3cos(3\u03c0(1((-3((-2x + 3)/(-3x + 4)) + 2)/(-1((-2x + 3)/(-3x + 4)) - 1))^2 - 5((-3((-2x + 3)/(-3x + 4)) + 2)/(-1((-2x + 3)/(-3x + 4)) - 1))) - 2) - 3) + 5) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-2|(-4(1|(2cos(3\u03c0((2x - 1)/(2x)) + 2) + 1) - 3| + 3)^2 - 4(1|(2cos(3\u03c0((2x - 1)/(2x)) + 2) + 1) - 3| + 3) + 2) + 3| + 2))/(-3(-2|(-4(1|(2cos(3\u03c0((2x - 1)/(2x)) + 2) + 1) - 3| + 3)^2 - 4(1|(2cos(3\u03c0((2x - 1)/(2x)) + 2) + 1) - 3| + 3) + 2) + 3| + 2) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-1cos(1\u03c0(-3|(-1(-5(-3x + 2)^2 - 3(-3x + 2) - 3) - 4) - 3| - 2) - 3) + 1) + 3| + 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(1|(-2|(-2sin(3\u03c0(2(-3x + 3)^2 + 2(-3x + 3) - 4) - 3) - 1) - 3| - 2)| + 2) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-2((3(1|(2(-1sin(1\u03c0x + 2)) - 5)| + 1) - 1)/(-2(1|(2(-1sin(1\u03c0x + 2)) - 5)| + 1) - 1))^2 + 4((3(1|(2(-1sin(1\u03c0x + 2)) - 5)| + 1) - 1)/(-2(1|(2(-1sin(1\u03c0x + 2)) - 5)| + 1) - 1)) + 4) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2sin(2\u03c0(-1(-2|(-1|(4(3|x - 2| - 3)^2 - 1) + 2| + 2) + 2| - 1) - 5) + 2) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3sin(3\u03c0(-2|((3(2(1|x - 1| + 1) - 1) - 1)/(-1(2(1|x - 1| + 1) - 1) - 3)) - 3| + 3) - 1) + 2) + 3| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(-1(2(-3sin(2\u03c0(-1((1x - 1)/(1x - 3))^2 + 3((1x - 1)/(1x - 3)) - 1) + 2)) - 2) - 2) + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2sin(3\u03c0((2(1|(-2|((2(-2|x + 3| + 3) - 1)/(-3(-2|x + 3| + 3) - 3))| - 3) + 3| - 1) + 1)/(-3(1|(-2|((2(-2|x + 3| + 3) - 1)/(-3(-2|x + 3| + 3) - 3))| - 3) + 3| - 1) - 1)) - 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(3sin(2\u03c0(3|(-1(1|(1x + 3) + 1| + 2)^2 - 2(1|(1x + 3) + 1| + 2) - 1) - 2|) - 1) + 1) - 1| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(-1(5(2cos(1\u03c0(-1|(-2x - 5)| - 3) - 2) - 1) - 3) + 5) - 3)/(-3(-1(5(2cos(1\u03c0(-1|(-2x - 5)| - 3) - 2) - 1) - 3) + 5) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1(2(1((2(-2sin(2\u03c0(-3x^2 - 5x + 3) + 3) - 3) + 1)/(1(-2sin(2\u03c0(-3x^2 - 5x + 3) + 3) - 3) + 2))^2 + 2((2(-2sin(2\u03c0(-3x^2 - 5x + 3) + 3) - 3) + 1)/(1(-2sin(2\u03c0(-3x^2 - 5x + 3) + 3) - 3) + 2)) + 3) - 2) - 4, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-2cos(2\u03c0(4(3|(-5((-1x + 2)/(3x + 2)) + 4) - 2|) - 2) - 1) + 2)^2 + 4(-2cos(2\u03c0(4(3|(-5((-1x + 2)/(3x + 2)) + 4) - 2|) - 2) - 1) + 2) + 5 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 4(1(-2|(4(2cos(2\u03c0(-5x + 4) - 2) - 1)^2 - 4(2cos(2\u03c0(-5x + 4) - 2) - 1) + 1) + 1| + 2)^2 + 2(-2|(4(2cos(2\u03c0(-5x + 4) - 2) - 1)^2 - 4(2cos(2\u03c0(-5x + 4) - 2) - 1) + 1) + 1| + 2) - 2)^2 - 5(1(-2|(4(2cos(2\u03c0(-5x + 4) - 2) - 1)^2 - 4(2cos(2\u03c0(-5x + 4) - 2) - 1) + 1) + 1| + 2)^2 + 2(-2|(4(2cos(2\u03c0(-5x + 4) - 2) - 1)^2 - 4(2cos(2\u03c0(-5x + 4) - 2) - 1) + 1) + 1| + 2) - 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1((3(1sin(3\u03c0(2(5(-2|x - 1| - 3) - 3)^2 - 3(5(-2|x - 1| - 3) - 3) - 1) - 3) - 3) - 1)/(-3(1sin(3\u03c0(2(5(-2|x - 1| - 3) - 3)^2 - 3(5(-2|x - 1| - 3) - 3) - 1) - 3) - 3) - 1)) - 2)/(1((3(1sin(3\u03c0(2(5(-2|x - 1| - 3) - 3)^2 - 3(5(-2|x - 1| - 3) - 3) - 1) - 3) - 3) - 1)/(-3(1sin(3\u03c0(2(5(-2|x - 1| - 3) - 3)^2 - 3(5(-2|x - 1| - 3) - 3) - 1) - 3) - 3) - 1)) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(1(1sin(2\u03c0(-3|(2|(-4x^2 + 4x - 3) + 3| + 3)| - 2) - 1) + 2)) + 1| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(2((3(-3(3cos(3\u03c0(2x - 3)) - 1) - 4) - 2)/(-2(-3(3cos(3\u03c0(2x - 3)) - 1) - 4) - 3))^2 - 4((3(-3(3cos(3\u03c0(2x - 3)) - 1) - 4) - 2)/(-2(-3(3cos(3\u03c0(2x - 3)) - 1) - 4) - 3)) - 1) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-3|(1|(1((2(1x - 1) + 1)/(2(1x - 1) - 3))^2 + 2((2(1x - 1) + 1)/(2(1x - 1) - 3)) - 4)|) - 2| + 1)| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2((-1(-3|(1|(5(3x^2 - 3)^2 + 3(3x^2 - 3)) - 3| - 3) - 3| + 3) - 1)/(2(-3|(1|(5(3x^2 - 3)^2 + 3(3x^2 - 3)) - 3| - 3) - 3| + 3) - 3)) - 1)/(-3((-1(-3|(1|(5(3x^2 - 3)^2 + 3(3x^2 - 3)) - 3| - 3) - 3| + 3) - 1)/(2(-3|(1|(5(3x^2 - 3)^2 + 3(3x^2 - 3)) - 3| - 3) - 3| + 3) - 3))) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-4(2((-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) + 1)/(-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) - 2)) + 4)^2 + 4(2((-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) + 1)/(-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) - 2)) + 4) - 4))/(2(-4(2((-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) + 1)/(-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) - 2)) + 4)^2 + 4(2((-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) + 1)/(-1(-1(3|x| - 3)^2 + 4(3|x| - 3) + 1) - 2)) + 4) - 4) + 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(-4(2(-2|(1|(-2x^2 + 4x + 2) - 3| + 3) - 3| + 1)^2 + 2(-2|(1|(-2x^2 + 4x + 2) - 3| + 3) - 3| + 1) - 5)) - 2)/(2(-4(2(-2|(1|(-2x^2 + 4x + 2) - 3| + 3) - 3| + 1)^2 + 2(-2|(1|(-2x^2 + 4x + 2) - 3| + 3) - 3| + 1) - 5)) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(-3(2|(5(-1|(1cos(1\u03c0x + 1)) - 1| + 1) - 1) + 1| + 1) - 3) - 2)/(3(-3(2|(5(-1|(1cos(1\u03c0x + 1)) - 1| + 1) - 1) + 1| + 1) - 3) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3cos(2\u03c0(3(1(-1((2(-3|x - 2| + 3) + 2)/(3(-3|x - 2| + 3))) - 3))^2 + 3(1(-1((2(-3|x - 2| + 3) + 2)/(3(-3|x - 2| + 3))) - 3)) - 1)) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-1|(-3|((3(-3sin(2\u03c0(-5x - 3) - 2) - 3) - 1)/(-3(-3sin(2\u03c0(-5x - 3) - 2) - 3) + 4)) - 1| - 2) + 1| - 2) - 1| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3sin(1\u03c0(-3|(4(4((2(3|x + 2|))/(3(3|x + 2|) - 1)) - 3)^2 - 5(4((2(3|x + 2|))/(3(3|x + 2|) - 1)) - 3) + 2) + 2| + 1) + 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-2sin(3\u03c0((-2((-1(5(1|x + 1| - 3) - 2) - 1)/(-1(5(1|x + 1| - 3) - 2) - 3)))/(-1((-1(5(1|x + 1| - 3) - 2) - 1)/(-1(5(1|x + 1| - 3) - 2) - 3)) - 3)) + 2) + 1)^2 - 3(-2sin(3\u03c0((-2((-1(5(1|x + 1| - 3) - 2) - 1)/(-1(5(1|x + 1| - 3) - 2) - 3)))/(-1((-1(5(1|x + 1| - 3) - 2) - 1)/(-1(5(1|x + 1| - 3) - 2) - 3)) - 3)) + 2) + 1) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2cos(3\u03c0((-3(1|((-2((1(-5x^2 - 2x - 3) - 3)/(2(-5x^2 - 2x - 3) - 1)) + 2)/(-1((1(-5x^2 - 2x - 3) - 3)/(2(-5x^2 - 2x - 3) - 1)) - 2)) + 2|) - 1)/(-1(1|((-2((1(-5x^2 - 2x - 3) - 3)/(2(-5x^2 - 2x - 3) - 1)) + 2)/(-1((1(-5x^2 - 2x - 3) - 3)/(2(-5x^2 - 2x - 3) - 1)) - 2)) + 2|) + 3)) + 1) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((3(-1cos(2\u03c0(-1|(5(-3|x + 2| - 3)^2 + 5(-3|x + 2| - 3) + 2) - 3| + 2) - 1)) + 2)/(2(-1cos(2\u03c0(-1|(5(-3|x + 2| - 3)^2 + 5(-3|x + 2| - 3) + 2) - 3| + 2) - 1)) - 1)) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-2(3|(-3(-1(2|((-1x + 3)/(3x - 1)) + 1| - 2)^2 + 5(2|((-1x + 3)/(3x - 1)) + 1| - 2) - 5)^2 + 2(-1(2|((-1x + 3)/(3x - 1)) + 1| - 2)^2 + 5(2|((-1x + 3)/(3x - 1)) + 1| - 2) - 5) + 3) - 2| + 2) - 3)/(-3(3|(-3(-1(2|((-1x + 3)/(3x - 1)) + 1| - 2)^2 + 5(2|((-1x + 3)/(3x - 1)) + 1| - 2) - 5)^2 + 2(-1(2|((-1x + 3)/(3x - 1)) + 1| - 2)^2 + 5(2|((-1x + 3)/(3x - 1)) + 1| - 2) - 5) + 3) - 2| + 2) - 1) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(-1(-2(-1sin(1\u03c0(5((-3x + 3)/(1x + 2)) - 4) - 2) + 3) - 1) + 3))/(-3(-1(-2(-1sin(1\u03c0(5((-3x + 3)/(1x + 2)) - 4) - 2) + 3) - 1) + 3) + 2) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3sin(3\u03c0(1(-1((2(-1(1|x - 2| + 2) - 1) + 3)/(-1(-1(1|x - 2| + 2) - 1) - 1))^2 + 5((2(-1(1|x - 2| + 2) - 1) + 3)/(-1(-1(1|x - 2| + 2) - 1) - 1)) - 3)^2 + 2(-1((2(-1(1|x - 2| + 2) - 1) + 3)/(-1(-1(1|x - 2| + 2) - 1) - 1))^2 + 5((2(-1(1|x - 2| + 2) - 1) + 3)/(-1(-1(1|x - 2| + 2) - 1) - 1)) - 3) - 3) - 3) + 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|((-3((1(-1|(-2|(2x^2 - 3x - 3) - 1| - 1)| + 3) + 2)/(2(-1|(-2|(2x^2 - 3x - 3) - 1| - 1)| + 3) - 1)) + 3)/(3((1(-1|(-2|(2x^2 - 3x - 3) - 1| - 1)| + 3) + 2)/(2(-1|(-2|(2x^2 - 3x - 3) - 1| - 1)| + 3) - 1)) - 1)) + 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-1|(1(-3|(-1sin(3\u03c0((-3x)/(-2x + 3)) - 1) + 2) + 2|)^2 - 1(-3|(-1sin(3\u03c0((-3x)/(-2x + 3)) - 1) + 2) + 2|) + 4) - 2| - 3) - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-5(1sin(3\u03c0(-1((3(-1|x|) - 1)/(-2(-1|x|) - 2)) - 5) + 2)))^2 - 5(-5(1sin(3\u03c0(-1((3(-1|x|) - 1)/(-2(-1|x|) - 2)) - 5) + 2))) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3(-2cos(3\u03c0(3(-2((2(5x + 2) - 1)/(1(5x + 2)))^2 - 4((2(5x + 2) - 1)/(1(5x + 2))) + 3)) - 1) - 3) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|((1(2|(2sin(3\u03c0(-4(-2|x + 2| - 2)^2 - 5(-2|x + 2| - 2) + 2) + 3) + 2) + 1|))/(-2(2|(2sin(3\u03c0(-4(-2|x + 2| - 2)^2 - 5(-2|x + 2| - 2) + 2) + 3) + 2) + 1|) - 3)) - 3| - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-1|((-1(1|(-1sin(1\u03c0((-1x)/(-2x + 3)) - 3) + 3) - 1| - 3) + 1)/(2(1|(-1sin(1\u03c0((-1x)/(-2x + 3)) - 3) + 3) - 1| - 3) + 2)) + 3| + 1)^2 + 3(-1|((-1(1|(-1sin(1\u03c0((-1x)/(-2x + 3)) - 3) + 3) - 1| - 3) + 1)/(2(1|(-1sin(1\u03c0((-1x)/(-2x + 3)) - 3) + 3) - 1| - 3) + 2)) + 3| + 1) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(-2|(-2(3|(-1sin(2\u03c0(5x^2 - 3x - 4) - 1) + 3) + 2| + 3) + 2) - 1| + 2))/(-2(-2|(-2(3|(-1sin(2\u03c0(5x^2 - 3x - 4) - 1) + 3) + 2| + 3) + 2) - 1| + 2) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((2((2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) + 3)/(-2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) - 2)) + 2)/(-1((2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) + 3)/(-2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) - 2)) - 3))^2 + 5((2((2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) + 3)/(-2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) - 2)) + 2)/(-1((2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) + 3)/(-2(2|((3(-1sin(2\u03c0x) - 1) - 1)/(-1(-1sin(2\u03c0x) - 1))) + 2| + 2) - 2)) - 3)) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(-3|(5(-2(3sin(3\u03c0(-1x^2 - 1x + 5) + 1) - 3) - 5)^2 + 1(-2(3sin(3\u03c0(-1x^2 - 1x + 5) + 1) - 3) - 5) - 4) - 1| - 1) + 2)/(3(-3|(5(-2(3sin(3\u03c0(-1x^2 - 1x + 5) + 1) - 3) - 5)^2 + 1(-2(3sin(3\u03c0(-1x^2 - 1x + 5) + 1) - 3) - 5) - 4) - 1| - 1)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|(-3(-2sin(2\u03c0(-1|(3|(2|x - 1| - 1) - 1| - 3) + 2|) - 3) - 2) - 4) + 1| + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3|(-2sin(3\u03c0(-1|(3(4(-3|x + 3| - 1) + 2) + 5) - 2| + 3) + 1) - 3) + 1| + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1(1|(1sin(3\u03c0((-1(-2(-2|x + 1| - 1)^2 - 2(-2|x + 1| - 1) + 3) + 3)/(-2(-2(-2|x + 1| - 1)^2 - 2(-2|x + 1| - 1) + 3) - 3)) - 2))| + 1) + 2)/(-2(1|(1sin(3\u03c0((-1(-2(-2|x + 1| - 1)^2 - 2(-2|x + 1| - 1) + 3) + 3)/(-2(-2(-2|x + 1| - 1)^2 - 2(-2|x + 1| - 1) + 3) - 3)) - 2))| + 1) - 2) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1((1(1|(-1sin(2\u03c0(3(1|x + 1| + 1)^2 - 5(1|x + 1| + 1) - 2) - 3) - 1) - 3| - 1) + 2)/(1(1|(-1sin(2\u03c0(3(1|x + 1| + 1)^2 - 5(1|x + 1| + 1) - 2) - 3) - 1) - 3| - 1) + 3))^2 + 4((1(1|(-1sin(2\u03c0(3(1|x + 1| + 1)^2 - 5(1|x + 1| + 1) - 2) - 3) - 1) - 3| - 1) + 2)/(1(1|(-1sin(2\u03c0(3(1|x + 1| + 1)^2 - 5(1|x + 1| + 1) - 2) - 3) - 1) - 3| - 1) + 3)) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-5(1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3))^2 + 1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3)) - 1)^2 + 1(1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3))^2 + 1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3)) - 1) - 2)^2 + 1(-5(1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3))^2 + 1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3)) - 1)^2 + 1(1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3))^2 + 1((3(3|(2|x| - 3) - 3|) - 1)/(2(3|(2|x| - 3) - 3|) + 3)) - 1) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(4(-3|((-1(-3((2x - 1)/(1x + 2))^2 + 1((2x - 1)/(1x + 2)) - 4) + 3)/(1(-3((2x - 1)/(1x + 2))^2 + 1((2x - 1)/(1x + 2)) - 4) + 2)) + 3| + 1)^2 + 5)^2 + 3(4(-3|((-1(-3((2x - 1)/(1x + 2))^2 + 1((2x - 1)/(1x + 2)) - 4) + 3)/(1(-3((2x - 1)/(1x + 2))^2 + 1((2x - 1)/(1x + 2)) - 4) + 2)) + 3| + 1)^2 + 5) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(1cos(2\u03c0(-1|(-2|(5(1x^2 + 5x + 5) - 4) - 3| - 3) + 1| - 1) - 2) + 1)^2 - 4(1cos(2\u03c0(-1|(-2|(5(1x^2 + 5x + 5) - 4) - 3| - 3) + 1| - 1) - 2) + 1) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-2|((1(1cos(3\u03c0(3((-1x - 2)/(3x - 2))^2 + 1) - 2)) + 3)/(2(1cos(3\u03c0(3((-1x - 2)/(3x - 2))^2 + 1) - 2)) - 1)) - 2| + 2) - 3)/(3(-2|((1(1cos(3\u03c0(3((-1x - 2)/(3x - 2))^2 + 1) - 2)) + 3)/(2(1cos(3\u03c0(3((-1x - 2)/(3x - 2))^2 + 1) - 2)) - 1)) - 2| + 2) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5(-3|(1(-1((3(3cos(3\u03c0x + 2) - 1))/(-3(3cos(3\u03c0x + 2) - 1) + 1)) - 4)^2 + 2) + 1| - 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(2|(3|(-3sin(1\u03c0(-1(1x - 3)^2 + 1(1x - 3) - 2) + 3) - 1) - 2| + 2)| + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1((-2(1|(-2|(-3cos(3\u03c0(1x - 2) - 1) + 1) - 1| - 3) - 3|) + 2)/(2(1|(-2|(-3cos(3\u03c0(1x - 2) - 1) + 1) - 1| - 3) - 3|))) + 3)/(-2((-2(1|(-2|(-3cos(3\u03c0(1x - 2) - 1) + 1) - 1| - 3) - 3|) + 2)/(2(1|(-2|(-3cos(3\u03c0(1x - 2) - 1) + 1) - 1| - 3) - 3|))) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-1((2(-2|(1cos(2\u03c0(3x^2 + 2x + 1)) - 1) - 3| + 1) + 1)/(1(-2|(1cos(2\u03c0(3x^2 + 2x + 1)) - 1) - 3| + 1) - 3))^2 + 5) + 3)/(1(-1((2(-2|(1cos(2\u03c0(3x^2 + 2x + 1)) - 1) - 3| + 1) + 1)/(1(-2|(1cos(2\u03c0(3x^2 + 2x + 1)) - 1) - 3| + 1) - 3))^2 + 5) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(4(-1(3(-1|(1|x + 2| - 3)| + 2)^2 + 1(-1|(1|x + 2| - 3)| + 2) - 1)^2 + 3(3(-1|(1|x + 2| - 3)| + 2)^2 + 1(-1|(1|x + 2| - 3)| + 2) - 1) - 3) + 1) - 3| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(-4(-3sin(1\u03c0(-1(1|(-3x^2 + 5x - 1) - 1| - 3) + 5) + 2)) + 2) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(1sin(3\u03c0(3(2|((-1(-1x + 1) - 2)/(2(-1x + 1) - 1)) - 2| + 1) - 3) - 2)) - 3| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(3\u03c0(5(-2((2(3(-5x - 3) + 5) - 2)/(1(3(-5x - 3) + 5))) + 3)^2 - 5(-2((2(3(-5x - 3) + 5) - 2)/(1(3(-5x - 3) + 5))) + 3) - 3) + 3) + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1sin(2\u03c0(5(-1|(-4((-1(-2|x - 2|) + 2)/(3(-2|x - 2|) + 1)) + 2) - 1| + 2) - 3) + 1) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(1|(-3|(-1sin(1\u03c0(5(-1|x - 2| - 2) + 1) + 3) - 3) + 3| - 3) + 1| - 2)^2 - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1(3sin(2\u03c0(2|(5(1|x - 3| - 1)^2 - 4(1|x - 3| - 1) - 4) + 3| + 3) - 3) + 2)^2 - 4(3sin(2\u03c0(2|(5(1|x - 3| - 1)^2 - 4(1|x - 3| - 1) - 4) + 3| + 3) - 3) + 2) - 3) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(4(-5(1sin(2\u03c0(-2|(2|x - 3| - 3) - 1| - 3) - 2) + 1) + 2) + 4) + 1| + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2e^(-1((-2(1|(1((-2(-1x^2 - 4x - 1) + 3)/(1(-1x^2 - 4x - 1) + 3))^2 - 4((-2(-1x^2 - 4x - 1) + 3)/(1(-1x^2 - 4x - 1) + 3)) - 5) + 1| + 1) + 3)/(-1(1|(1((-2(-1x^2 - 4x - 1) + 3)/(1(-1x^2 - 4x - 1) + 3))^2 - 4((-2(-1x^2 - 4x - 1) + 3)/(1(-1x^2 - 4x - 1) + 3)) - 5) + 1| + 1) + 2))) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1cos(3\u03c0((3(-1|(1(2(1x^2 + 1x - 3)^2 - 4(1x^2 + 1x - 3) - 5)^2 - 4(2(1x^2 + 1x - 3)^2 - 4(1x^2 + 1x - 3) - 5) - 5) + 2| + 3) - 3)/(-2(-1|(1(2(1x^2 + 1x - 3)^2 - 4(1x^2 + 1x - 3) - 5)^2 - 4(2(1x^2 + 1x - 3)^2 - 4(1x^2 + 1x - 3) - 5) - 5) + 2| + 3) - 3)) + 2) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(1((3(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) + 1)/(-1(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) - 1))^2 + 4((3(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) + 1)/(-1(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) - 1)) - 3)^2 + 1(1((3(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) + 1)/(-1(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) - 1))^2 + 4((3(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) + 1)/(-1(-1|(3(2|x| - 1)^2 - 4(2|x| - 1) - 1) + 1| - 2) - 1)) - 3) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1sin(1\u03c0(-3(5(-5(1x - 5) + 4)^2 - 5(-5(1x - 5) + 4) + 1) + 5) + 1) + 3) + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2cos(1\u03c0(4(-2((-1(3|(-4x^2 + 1x + 5) + 3|) - 2)/(2(3|(-4x^2 + 1x + 5) + 3|) + 3)) - 5)^2 - 5(-2((-1(3|(-4x^2 + 1x + 5) + 3|) - 2)/(2(3|(-4x^2 + 1x + 5) + 3|) + 3)) - 5)) + 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(2\u03c0(3|(1|((-2(1(-5x^2 - 1x + 3)^2 - 5(-5x^2 - 1x + 3) - 3) - 3)/(-2(1(-5x^2 - 1x + 3)^2 - 5(-5x^2 - 1x + 3) - 3) + 3)) - 2| - 1)| - 3)) - 1 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(-3(4(3(-2|(2sin(2\u03c0x - 1) + 2) - 2| + 3) + 1) + 2)^2 - 5) - 3)/(2(-3(4(3(-2|(2sin(2\u03c0x - 1) + 2) - 2| + 3) + 1) + 2)^2 - 5) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3sin(1\u03c0(-4(5(5((-3(1x^2 + 5x - 1) - 1)/(-1(1x^2 + 5x - 1)))^2 - 3((-3(1x^2 + 5x - 1) - 1)/(-1(1x^2 + 5x - 1))) - 4) - 2) + 4) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-1(-4(-4(-3|(2sin(1\u03c0x - 2) + 3)| + 3) + 5) - 2)^2 + 5(-4(-4(-3|(2sin(1\u03c0x - 2) + 3)| + 3) + 5) - 2) - 2))/(1(-1(-4(-4(-3|(2sin(1\u03c0x - 2) + 3)| + 3) + 5) - 2)^2 + 5(-4(-4(-3|(2sin(1\u03c0x - 2) + 3)| + 3) + 5) - 2) - 2) + 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1|(4(-1|(-3(-1cos(2\u03c0x) - 2) - 1)| - 3)^2) - 1| + 3)| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(-2|(1sin(1\u03c0((-2((1((-2x - 2)/(1x)) - 2)/(2((-2x - 2)/(1x)) + 1)) + 3)/(1((1((-2x - 2)/(1x)) - 2)/(2((-2x - 2)/(1x)) + 1)) - 2)) - 2) + 3) - 1| + 2) - 2| - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1|(-5(-2sin(3\u03c0((2(-2|x - 1| + 2) - 1)/(-2(-2|x - 1| + 2) - 2))))^2 + 5(-2sin(3\u03c0((2(-2|x - 1| + 2) - 1)/(-2(-2|x - 1| + 2) - 2)))) - 2)|)^2 + 4(-1|(-5(-2sin(3\u03c0((2(-2|x - 1| + 2) - 1)/(-2(-2|x - 1| + 2) - 2))))^2 + 5(-2sin(3\u03c0((2(-2|x - 1| + 2) - 1)/(-2(-2|x - 1| + 2) - 2)))) - 2)|) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-1(2|(-4((-1(-1sin(1\u03c0x - 3) - 2) + 3)/(1(-1sin(1\u03c0x - 3) - 2))) - 5) - 2| - 2) - 4) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3(1|((3(3sin(1\u03c0(3(2x - 2) - 3) + 2)) - 3)/(3(3sin(1\u03c0(3(2x - 2) - 3) + 2))))| + 2) + 5, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((-3(1|(-3cos(3\u03c0((3(4x + 1) + 1)/(-3(4x + 1) + 4)) + 1)) - 2| + 3) - 3)/(-1(1|(-3cos(3\u03c0((3(4x + 1) + 1)/(-3(4x + 1) + 4)) + 1)) - 2| + 3) - 3)) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-2(1sin(3\u03c0(3|(2(-5(1x - 2)^2 + 2(1x - 2) - 2)^2 - 3(-5(1x - 2)^2 + 2(1x - 2) - 2) - 3) - 2| - 1) - 1) + 1))/(-2(1sin(3\u03c0(3|(2(-5(1x - 2)^2 + 2(1x - 2) - 2)^2 - 3(-5(1x - 2)^2 + 2(1x - 2) - 2) - 3) - 2| - 1) - 1) + 1) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(3|(2sin(1\u03c0(-3((3(4x))/(1(4x) + 1)) - 3) - 2) + 2) - 3| + 3) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-4(-4(2|((3(1cos(1\u03c0x + 3) - 2) + 3)/(2(1cos(1\u03c0x + 3) - 2) - 1)) - 1| - 1)^2 + 5(2|((3(1cos(1\u03c0x + 3) - 2) + 3)/(2(1cos(1\u03c0x + 3) - 2) - 1)) - 1| - 1) + 5) + 2)| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3(-5((-1(4(2cos(2\u03c0x + 3))^2 - 3(2cos(2\u03c0x + 3)) + 1) + 1)/(2(4(2cos(2\u03c0x + 3))^2 - 3(2cos(2\u03c0x + 3)) + 1) + 2)) - 3) - 3) - 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-2sin(1\u03c0(-5(1|(2(-2|x + 2| - 3) + 2) - 3| - 3)^2 + 5(1|(2(-2|x + 2| - 3) + 2) - 3| - 3) - 4) + 3) - 1) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(1|((-2(1(2cos(2\u03c0(-4x - 2) + 1) - 1) - 5) + 2)/(1(1(2cos(2\u03c0(-4x - 2) + 1) - 1) - 5) - 2)) + 1| - 2) - 1| + 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(5(-2sin(3\u03c0((-1(-1|(-1x + 4) - 3| + 3) - 2)/(3(-1|(-1x + 4) - 3| + 3) + 2)) - 1) - 1)^2 - 4(-2sin(3\u03c0((-1(-1|(-1x + 4) - 3| + 3) - 2)/(3(-1|(-1x + 4) - 3| + 3) + 2)) - 1) - 1) - 3) + 1)/(2(5(-2sin(3\u03c0((-1(-1|(-1x + 4) - 3| + 3) - 2)/(3(-1|(-1x + 4) - 3| + 3) + 2)) - 1) - 1)^2 - 4(-2sin(3\u03c0((-1(-1|(-1x + 4) - 3| + 3) - 2)/(3(-1|(-1x + 4) - 3| + 3) + 2)) - 1) - 1) - 3) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1((3(-2cos(2\u03c0((-1(-1(1x + 1) + 5))/(-1(-1(1x + 1) + 5) - 1)) - 3) - 3) - 2)/(2(-2cos(2\u03c0((-1(-1(1x + 1) + 5))/(-1(-1(1x + 1) + 5) - 1)) - 3) - 3) - 3))^2 - 4((3(-2cos(2\u03c0((-1(-1(1x + 1) + 5))/(-1(-1(1x + 1) + 5) - 1)) - 3) - 3) - 2)/(2(-2cos(2\u03c0((-1(-1(1x + 1) + 5))/(-1(-1(1x + 1) + 5) - 1)) - 3) - 3) - 3)) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2|(-4(2sin(2\u03c0(1|((-3((-3x + 1)/(1x + 1)) - 2)/(1((-3x + 1)/(1x + 1)) + 3)) - 1| - 2) + 1)) - 2) + 3| - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(2(-2|((-3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3) - 2)/(3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3)))| - 2)^2 + 5(-2|((-3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3) - 2)/(3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3)))| - 2))^2 - 5(2(-2|((-3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3) - 2)/(3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3)))| - 2)^2 + 5(-2|((-3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3) - 2)/(3(-2cos(3\u03c0((1x)/(-1x + 3)) + 2) - 3)))| - 2)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(4(1(-4(-2cos(2\u03c0(2x) + 1) + 1) - 3) - 3) - 4)| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((1(-1(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3)^2 + 2(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3) + 5) + 3)/(2(-1(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3)^2 + 2(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3) + 5)))^2 + 4((1(-1(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3)^2 + 2(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3) + 5) + 3)/(2(-1(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3)^2 + 2(1sin(3\u03c0(-4(-1x + 4)^2 - 4(-1x + 4) + 1) - 2) + 3) + 5))) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(3(2|(-1((2(-3|x + 2| + 2) - 2)/(-2(-3|x + 2| + 2) - 3))^2 - 1((2(-3|x + 2| + 2) - 2)/(-2(-3|x + 2| + 2) - 3)) + 4) - 3| + 3) + 2) - 2| + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(1(2sin(3\u03c0(3|(2|(3x^2 - 1x + 1) + 2| - 1) + 3|) - 2)))| + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1sin(2\u03c0(1|(1|(2|(1x^2 - 1x - 5) + 3|) + 3| - 1)|) + 2) - 2) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1|(2|(1(-2cos(3\u03c0(-5(1x - 5) + 5) - 2) - 2)^2 + 5(-2cos(3\u03c0(-5(1x - 5) + 5) - 2) - 2))|) - 1| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "84", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-2sin(2\u03c0(1((2((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) - 2)/(-1((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) + 2))^2 - 4((2((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) - 2)/(-1((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) + 2)) - 1) - 3) + 1) - 3)/(1(-2sin(2\u03c0(1((2((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) - 2)/(-1((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) + 2))^2 - 4((2((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) - 2)/(-1((2((1x)/(-2x + 3)) + 1)/(3((1x)/(-2x + 3)) + 3)) + 2)) - 1) - 3) + 1) - 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-3|((2(-3sin(1\u03c0(-3(-2x + 5) - 1) + 3)) + 2)/(-2(-3sin(1\u03c0(-3(-2x + 5) - 1) + 3)) + 3))| + 1) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|((-2(2cos(1\u03c0(5(-2(2|x + 3| - 3) + 5)^2 + 2) - 1) + 1) + 2)/(-2(2cos(1\u03c0(5(-2(2|x + 3| - 3) + 5)^2 + 2) - 1) + 1) + 3)) + 1| + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2((-2(-3|(-2cos(2\u03c0(2|((-3x - 3)/(1x + 3)) + 2| + 2) + 3) + 3) + 3|) - 1)/(-1(-3|(-2cos(2\u03c0(2|((-3x - 3)/(1x + 3)) + 2| + 2) + 3) + 3) + 3|) + 2))^2 + 1((-2(-3|(-2cos(2\u03c0(2|((-3x - 3)/(1x + 3)) + 2| + 2) + 3) + 3) + 3|) - 1)/(-1(-3|(-2cos(2\u03c0(2|((-3x - 3)/(1x + 3)) + 2| + 2) + 3) + 3) + 3|) + 2)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3sin(2\u03c0(2(-2((1(-2(3x^2 + 3x + 1)) - 1)/(-3(-2(3x^2 + 3x + 1)) - 2))^2 - 5((1(-2(3x^2 + 3x + 1)) - 1)/(-3(-2(3x^2 + 3x + 1)) - 2)) + 5)^2 + 1) - 1) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-2((-1(3(1cos(2\u03c0(-4x + 2) + 1)) + 5) - 1)/(-3(3(1cos(2\u03c0(-4x + 2) + 1)) + 5) - 1))^2 + 3((-1(3(1cos(2\u03c0(-4x + 2) + 1)) + 5) - 1)/(-3(3(1cos(2\u03c0(-4x + 2) + 1)) + 5) - 1)) + 1)| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|((2((1((-3(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 2)/(1(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 1)) - 1)/(2((-3(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 2)/(1(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 1)))) - 1)/(3((1((-3(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 2)/(1(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 1)) - 1)/(2((-3(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 2)/(1(-2(-1cos(3\u03c0x + 3) - 3)^2 + 1(-1cos(3\u03c0x + 3) - 3) + 2) + 1)))) - 2)) + 2| - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(-4(1|(-3|(-1cos(2\u03c0(3x + 1) + 3) - 3) - 2|) - 2| + 3) - 3) - 3| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 5(2|(2sin(2\u03c0((-2((-3(-3x + 4) - 3)/(-2(-3x + 4))) + 3)/(2((-3(-3x + 4) - 3)/(-2(-3x + 4))) - 1)) + 3) - 3) - 2| + 1) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|((-2(3(2sin(2\u03c0(5(3|x - 2| - 2)^2 + 5(3|x - 2| - 2) - 4) + 2))^2 - 4(2sin(2\u03c0(5(3|x - 2| - 2)^2 + 5(3|x - 2| - 2) - 4) + 2)) + 1) + 3)/(-3(3(2sin(2\u03c0(5(3|x - 2| - 2)^2 + 5(3|x - 2| - 2) - 4) + 2))^2 - 4(2sin(2\u03c0(5(3|x - 2| - 2)^2 + 5(3|x - 2| - 2) - 4) + 2)) + 1) + 2)) + 2|, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2((1(2(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|)^2 - 5(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|) + 4) + 1)/(3(2(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|)^2 - 5(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|) + 4) - 1)) + 3)/(-1((1(2(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|)^2 - 5(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|) + 4) + 1)/(3(2(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|)^2 - 5(2|(-2sin(3\u03c0(-3x^2 + 5x - 2) + 3) - 2)|) + 4) - 1)) - 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3cos(3\u03c0(-2|((-1(1((-3(1|x - 1| + 3) + 2)/(-2(1|x - 1| + 3) - 3))^2 - 3) + 1)/(1(1((-3(1|x - 1| + 3) + 2)/(-2(1|x - 1| + 3) - 3))^2 - 3) + 1)) - 3| - 3)) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -5(-2e^(1((-1(-2|(-2(-5x^2 + 4x + 4)^2 + 5(-5x^2 + 4x + 4) + 5)| - 2) - 2)/(-3(-2|(-2(-5x^2 + 4x + 4)^2 + 5(-5x^2 + 4x + 4) + 5)| - 2) + 1))) - 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2|((3(2sin(3\u03c0(-1|(5((1x - 3)/(-3x - 3))^2 + 3((1x - 3)/(-3x - 3)) + 4) - 2| - 2) - 2) - 1))/(-3(2sin(3\u03c0(-1|(5((1x - 3)/(-3x - 3))^2 + 3((1x - 3)/(-3x - 3)) + 4) - 2| - 2) - 2) - 1) - 1)) + 2| - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1((-2(-4(-1(3cos(2\u03c0(3|x - 1| + 1)) - 1) + 2) + 1) - 2)/(1(-4(-1(3cos(2\u03c0(3|x - 1| + 1)) - 1) + 2) + 1) - 2))^2 + 1((-2(-4(-1(3cos(2\u03c0(3|x - 1| + 1)) - 1) + 2) + 1) - 2)/(1(-4(-1(3cos(2\u03c0(3|x - 1| + 1)) - 1) + 2) + 1) - 2)) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(4(-2(-1|(-2|((1x)/(-2x + 3))| + 2) - 1| + 2)^2 - 2(-1|(-2|((1x)/(-2x + 3))| + 2) - 1| + 2))^2 + 5(-2(-1|(-2|((1x)/(-2x + 3))| + 2) - 1| + 2)^2 - 2(-1|(-2|((1x)/(-2x + 3))| + 2) - 1| + 2)) - 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4((-1(1(-1(-3cos(1\u03c0(-3x^2 + 3x - 1) + 3) + 1) - 5) - 5) + 3)/(1(1(-1(-3cos(1\u03c0(-3x^2 + 3x - 1) + 3) + 1) - 5) - 5) + 2)) + 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(1|(4(-1((-1(-2sin(3\u03c0x + 2) - 2) + 2)/(1(-2sin(3\u03c0x + 2) - 2) - 3))^2 + 4((-1(-2sin(3\u03c0x + 2) - 2) + 2)/(1(-2sin(3\u03c0x + 2) - 2) - 3)) + 5) + 3) - 2| - 1) + 2)/(1(1|(4(-1((-1(-2sin(3\u03c0x + 2) - 2) + 2)/(1(-2sin(3\u03c0x + 2) - 2) - 3))^2 + 4((-1(-2sin(3\u03c0x + 2) - 2) + 2)/(1(-2sin(3\u03c0x + 2) - 2) - 3)) + 5) + 3) - 2| - 1) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(2(-2|(1(2|((1x - 2)/(1x)) + 1|) - 2) - 2| + 2)^2 + 2(-2|(1(2|((1x - 2)/(1x)) + 1|) - 2) - 2| + 2) + 4) - 2)/(1(2(-2|(1(2|((1x - 2)/(1x)) + 1|) - 2) - 2| + 2)^2 + 2(-2|(1(2|((1x - 2)/(1x)) + 1|) - 2) - 2| + 2) + 4) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (1(3(-3|(-3(-2(1sin(1\u03c0x + 1) - 3)^2 - 3(1sin(1\u03c0x + 1) - 3) - 3) - 4) + 2| + 3)^2 + 3(-3|(-3(-2(1sin(1\u03c0x + 1) - 3)^2 - 3(1sin(1\u03c0x + 1) - 3) - 3) - 4) + 2| + 3) + 1) + 2)/(2(3(-3|(-3(-2(1sin(1\u03c0x + 1) - 3)^2 - 3(1sin(1\u03c0x + 1) - 3) - 3) - 4) + 2| + 3)^2 + 3(-3|(-3(-2(1sin(1\u03c0x + 1) - 3)^2 - 3(1sin(1\u03c0x + 1) - 3) - 3) - 4) + 2| + 3) + 1) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1cos(3\u03c0(-1(2|((1(-4(2x^2 - 3x - 1) + 1) - 1)/(2(-4(2x^2 - 3x - 1) + 1) + 1)) - 2| - 1)^2 + 1(2|((1(-4(2x^2 - 3x - 1) + 1) - 1)/(2(-4(2x^2 - 3x - 1) + 1) + 1)) - 2| - 1) + 4) - 3) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-1cos(2\u03c0(5((-3((-2(-3|x - 3| - 1) - 1)/(2(-3|x - 3| - 1) - 1)) - 2)/(-1((-2(-3|x - 3| - 1) - 1)/(2(-3|x - 3| - 1) - 1))))^2 + 3((-3((-2(-3|x - 3| - 1) - 1)/(2(-3|x - 3| - 1) - 1)) - 2)/(-1((-2(-3|x - 3| - 1) - 1)/(2(-3|x - 3| - 1) - 1)))) - 2) - 2) - 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|((-3(-3|(-3|(1(2cos(1\u03c0x + 2) + 1)^2 + 3(2cos(1\u03c0x + 2) + 1) - 5) + 2| - 3) + 2| + 1) + 3)/(1(-3|(-3|(1(2cos(1\u03c0x + 2) + 1)^2 + 3(2cos(1\u03c0x + 2) + 1) - 5) + 2| - 3) + 2| + 1) + 2)) - 2| + 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(-2|(-2(2|((1(-1cos(1\u03c0x - 2) - 2))/(-2(-1cos(1\u03c0x - 2) - 2) + 3))|)^2 + 1(2|((1(-1cos(1\u03c0x - 2) - 2))/(-2(-1cos(1\u03c0x - 2) - 2) + 3))|) - 1) + 3|) + 1| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-2(-3|((-3(2cos(1\u03c0(2x)) + 3) - 3)/(-1(2cos(1\u03c0(2x)) + 3) - 3)) + 2| + 2)^2 - 2(-3|((-3(2cos(1\u03c0(2x)) + 3) - 3)/(-1(2cos(1\u03c0(2x)) + 3) - 3)) + 2| + 2) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (3(-1(5((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1))^2 + 1((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1)) + 5)^2 + 4(5((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1))^2 + 1((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1)) + 5) - 5) - 2)/(1(-1(5((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1))^2 + 1((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1)) + 5)^2 + 4(5((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1))^2 + 1((2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 3)/(2(4(2sin(1\u03c0x - 2) + 1)^2 - 2(2sin(1\u03c0x - 2) + 1) + 5) - 1)) + 5) - 5)), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(-1|(-2(4(3|(1|x + 3| + 3) - 3|) - 3)^2 - 3(4(3|(1|x + 3| + 3) - 3|) - 3) + 3) + 2| - 2) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3|(-1(-1|((-1(3sin(2\u03c0((3x + 2)/(-3x + 2)) - 2)) - 3)/(1(3sin(2\u03c0((3x + 2)/(-3x + 2)) - 2)) + 2)) - 3| + 1) + 5) - 1|, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-1((2((2(-3(3cos(3\u03c0x) + 2) - 2))/(2(-3(3cos(3\u03c0x) + 2) - 2) - 1)) - 3)/(-2((2(-3(3cos(3\u03c0x) + 2) - 2))/(2(-3(3cos(3\u03c0x) + 2) - 2) - 1)) - 3))^2 + 4) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4((1(5(-3|(-1(5x^2 + 4x - 3)^2 + 4(5x^2 + 4x - 3) + 5) + 3| - 1)) + 3)/(3(5(-3|(-1(5x^2 + 4x - 3)^2 + 4(5x^2 + 4x - 3) + 5) + 3| - 1)) - 2)) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 3cos(3\u03c0(-4(-2|(-4(2((-2x + 2)/(3x + 1))^2 + 3((-2x + 2)/(3x + 1)))^2 - 1(2((-2x + 2)/(3x + 1))^2 + 3((-2x + 2)/(3x + 1))) - 4) + 3| + 3) - 4) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(-3|(-2(1|(2|(-3sin(1\u03c0x - 2) + 3) - 1| - 3)| - 3) - 1) + 3|) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(2|(1(-2|((1(2cos(2\u03c0x + 3) + 1) - 3)/(2(2cos(2\u03c0x + 3) + 1) + 1)) + 1| - 2) - 3)| - 2) + 1)/(-2(2|(1(-2|((1(2cos(2\u03c0x + 3) + 1) - 3)/(2(2cos(2\u03c0x + 3) + 1) + 1)) + 1| - 2) - 3)| - 2)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(1sin(2\u03c0(3(4(-3|(-2x + 1) + 2| - 2)^2 - 2(-3|(-2x + 1) + 2| - 2) - 2)^2 - 4(4(-3|(-2x + 1) + 2| - 2)^2 - 2(-3|(-2x + 1) + 2| - 2) - 2) + 3) - 1) + 2) + 2)/(2(1sin(2\u03c0(3(4(-3|(-2x + 1) + 2| - 2)^2 - 2(-3|(-2x + 1) + 2| - 2) - 2)^2 - 4(4(-3|(-2x + 1) + 2| - 2)^2 - 2(-3|(-2x + 1) + 2| - 2) - 2) + 3) - 1) + 2) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2((2(1(3(1|x - 2| - 2) + 1)^2 + 3(3(1|x - 2| - 2) + 1) + 4))/(2(1(3(1|x - 2| - 2) + 1)^2 + 3(3(1|x - 2| - 2) + 1) + 4) - 3)) - 2)^2 + 5(2((2(1(3(1|x - 2| - 2) + 1)^2 + 3(3(1|x - 2| - 2) + 1) + 4))/(2(1(3(1|x - 2| - 2) + 1)^2 + 3(3(1|x - 2| - 2) + 1) + 4) - 3)) - 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (2(-5(1(-5(-3cos(2\u03c0(4x^2 + 5x + 3) - 2) + 2) - 2)^2 - 4(-5(-3cos(2\u03c0(4x^2 + 5x + 3) - 2) + 2) - 2) - 5) - 1))/(2(-5(1(-5(-3cos(2\u03c0(4x^2 + 5x + 3) - 2) + 2) - 2)^2 - 4(-5(-3cos(2\u03c0(4x^2 + 5x + 3) - 2) + 2) - 2) - 5) - 1) - 3) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(4(-3|(-1|(1|(-1cos(1\u03c0x - 1) + 3) + 2| + 2) - 1| + 1) - 1| + 3)^2 + 4)| - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(4(-2|(-1(-2cos(3\u03c0(-2|x + 2| + 3) + 3) - 1) - 1) + 3|)) + 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -5(-2|(3sin(3\u03c0(-5(2((-1x - 1)/(3x - 1)) - 5) + 1) + 1)) - 3| + 2) + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(2(5(-2|(1sin(3\u03c0(5x^2 + 2x + 3) + 3) - 1)| + 1) + 3) - 3) + 2| is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2cos(2\u03c0(-5(-1((-1((3(3x - 5) + 2)/(1(3x - 5) + 2)) - 2)/(-3((3(3x - 5) + 2)/(1(3x - 5) + 2)))) + 2)^2 + 4) + 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-4((2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1) + 3)/(-2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1)))^2 - 5((2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1) + 3)/(-2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1))) - 1)^2 + 1(-4((2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1) + 3)/(-2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1)))^2 - 5((2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1) + 3)/(-2(3sin(3\u03c0(3(-2x^2 + 5x + 3) - 4) + 3) - 1))) - 1) - 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-2|((3(-2cos(2\u03c0(3|((-2x - 2)/(-2x + 1)) - 1| - 3) - 1) + 1) + 2)/(1(-2cos(2\u03c0(3|((-2x - 2)/(-2x + 1)) - 1| - 3) - 1) + 1)))| - 2))/(3(-2|((3(-2cos(2\u03c0(3|((-2x - 2)/(-2x + 1)) - 1| - 3) - 1) + 1) + 2)/(1(-2cos(2\u03c0(3|((-2x - 2)/(-2x + 1)) - 1| - 3) - 1) + 1)))| - 2) + 1) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1((-1(4(-5(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1)^2 + 3(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1) - 4)^2 - 3(-5(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1)^2 + 3(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1) - 4) + 2) + 1)/(3(4(-5(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1)^2 + 3(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1) - 4)^2 - 3(-5(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1)^2 + 3(-2(2cos(2\u03c0x + 3) + 2)^2 + 4(2cos(2\u03c0x + 3) + 2) - 1) - 4) + 2) + 3)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|((1(2(1|(2|(-2x^2 + 1x + 4) + 3| - 3) - 2| + 1) + 5))/(-2(2(1|(2|(-2x^2 + 1x + 4) + 3| - 3) - 2| + 1) + 5) + 3)) - 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 3(-1sin(1\u03c0(5(5((2(2x + 1) + 1)/(-3(2x + 1) - 1))^2 + 5((2(2x + 1) + 1)/(-3(2x + 1) - 1)) + 2)^2 - 1(5((2(2x + 1) + 1)/(-3(2x + 1) - 1))^2 + 5((2(2x + 1) + 1)/(-3(2x + 1) - 1)) + 2) - 1) + 1) + 2)^2 - 4(-1sin(1\u03c0(5(5((2(2x + 1) + 1)/(-3(2x + 1) - 1))^2 + 5((2(2x + 1) + 1)/(-3(2x + 1) - 1)) + 2)^2 - 1(5((2(2x + 1) + 1)/(-3(2x + 1) - 1))^2 + 5((2(2x + 1) + 1)/(-3(2x + 1) - 1)) + 2) - 1) + 1) + 2) - 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3(-5((-3(3(-3(3cos(1\u03c0x - 2) + 3) - 4) + 2) - 2)/(1(3(-3(3cos(1\u03c0x - 2) + 3) - 4) + 2)))^2 + 5((-3(3(-3(3cos(1\u03c0x - 2) + 3) - 4) + 2) - 2)/(1(3(-3(3cos(1\u03c0x - 2) + 3) - 4) + 2))) + 3) + 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-5(-2|(-3(-3(-5x^2 + 2x + 1)^2 - 5(-5x^2 + 2x + 1) + 5)^2 + 5(-3(-5x^2 + 2x + 1)^2 - 5(-5x^2 + 2x + 1) + 5) + 3) - 3| + 2) + 2) + 2)/(1(-5(-2|(-3(-3(-5x^2 + 2x + 1)^2 - 5(-5x^2 + 2x + 1) + 5)^2 + 5(-3(-5x^2 + 2x + 1)^2 - 5(-5x^2 + 2x + 1) + 5) + 3) - 3| + 2) + 2)) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-1((-1((3(2cos(2\u03c0((-1x - 3)/(-3x + 1)) + 2) + 1) + 1)/(-2(2cos(2\u03c0((-1x - 3)/(-3x + 1)) + 2) + 1) - 3)) - 3)/(-3((3(2cos(2\u03c0((-1x - 3)/(-3x + 1)) + 2) + 1) + 1)/(-2(2cos(2\u03c0((-1x - 3)/(-3x + 1)) + 2) + 1) - 3)) - 2)) - 4) + 4 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(-1((2(-5(-2cos(2\u03c0(-1|x - 3| + 3) - 3))^2 + 2(-2cos(2\u03c0(-1|x - 3| + 3) - 3)) + 2) + 2)/(2(-5(-2cos(2\u03c0(-1|x - 3| + 3) - 3))^2 + 2(-2cos(2\u03c0(-1|x - 3| + 3) - 3)) + 2) - 3))^2 + 4((2(-5(-2cos(2\u03c0(-1|x - 3| + 3) - 3))^2 + 2(-2cos(2\u03c0(-1|x - 3| + 3) - 3)) + 2) + 2)/(2(-5(-2cos(2\u03c0(-1|x - 3| + 3) - 3))^2 + 2(-2cos(2\u03c0(-1|x - 3| + 3) - 3)) + 2) - 3)) + 2) + 2| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(1cos(3\u03c0((-3((2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)))/(2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)) + 3)) - 1)/(-1((2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)))/(2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)) + 3))))) - 1))/(2(1cos(3\u03c0((-3((2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)))/(2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)) + 3)) - 1)/(-1((2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)))/(2((1(-4x + 2) + 3)/(-1(-4x + 2) - 1)) + 3))))) - 1) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(5((1(3cos(3\u03c0(-2(-2|x - 1| - 1) + 1) + 2) + 2) + 1)/(-2(3cos(3\u03c0(-2(-2|x - 1| - 1) + 1) + 2) + 2) + 1))^2 - 4((1(3cos(3\u03c0(-2(-2|x - 1| - 1) + 1) + 2) + 2) + 1)/(-2(3cos(3\u03c0(-2(-2|x - 1| - 1) + 1) + 2) + 2) + 1)) + 3) - 3| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(-2(-5((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3))^2 + 1((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3)) + 1)^2 - 3(-5((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3))^2 + 1((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3)) + 1) + 4))/(1(-2(-5((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3))^2 + 1((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3)) + 1)^2 - 3(-5((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3))^2 + 1((1((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)))/(-2((-1(-5x^2 + 3x + 5) + 3)/(1(-5x^2 + 3x + 5) - 2)) - 3)) + 1) + 4) + 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(-2|((2(2|(5(-1x)^2 - 2(-1x) - 1) - 1| - 1) + 1)/(-1(2|(5(-1x)^2 - 2(-1x) - 1) - 1| - 1) + 3)) + 1| - 1) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|((-2(3|(-3((-1(1sin(1\u03c0x - 1) + 3) - 3)/(-2(1sin(1\u03c0x - 1) + 3) - 3)) - 3) - 3| - 3))/(3(3|(-3((-1(1sin(1\u03c0x - 1) + 3) - 3)/(-2(1sin(1\u03c0x - 1) + 3) - 3)) - 3) - 3| - 3) + 3)) - 2| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(-2|(5(1(-3cos(2\u03c0((2x)/(-2x - 3)) + 3) + 2)^2 + 2(-3cos(2\u03c0((2x)/(-2x - 3)) + 3) + 2) + 1) - 3) - 1| + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1sin(1\u03c0(1((3(3(3|(-2x - 5) - 2| - 2)^2 + 2(3|(-2x - 5) - 2| - 2) + 4) + 3)/(-1(3(3|(-2x - 5) - 2| - 2)^2 + 2(3|(-2x - 5) - 2| - 2) + 4) - 2))^2 - 2((3(3(3|(-2x - 5) - 2| - 2)^2 + 2(3|(-2x - 5) - 2| - 2) + 4) + 3)/(-1(3(3|(-2x - 5) - 2| - 2)^2 + 2(3|(-2x - 5) - 2| - 2) + 4) - 2)) + 5) + 2) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (1((-3(2(-1cos(3\u03c0((-3(1x^2 + 5x - 2))/(-2(1x^2 + 5x - 2) + 1)) - 3) - 3) + 2) + 1)/(2(2(-1cos(3\u03c0((-3(1x^2 + 5x - 2))/(-2(1x^2 + 5x - 2) + 1)) - 3) - 3) + 2))) - 3)/(2((-3(2(-1cos(3\u03c0((-3(1x^2 + 5x - 2))/(-2(1x^2 + 5x - 2) + 1)) - 3) - 3) + 2) + 1)/(2(2(-1cos(3\u03c0((-3(1x^2 + 5x - 2))/(-2(1x^2 + 5x - 2) + 1)) - 3) - 3) + 2)))) negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-4(3(-1(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1)^2 - 4(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1) + 2)^2 - 2(-1(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1)^2 - 4(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1) + 2) - 3) - 4))/(1(-4(3(-1(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1)^2 - 4(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1) + 2)^2 - 2(-1(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1)^2 - 4(-1|(2sin(1\u03c0x - 3) - 1) + 2| - 1) + 2) - 3) - 4) - 3) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2(1((-1(-3cos(1\u03c0(3((1x - 2)/(1x + 3))^2 + 5((1x - 2)/(1x + 3)) + 2) - 1) - 2) - 3)/(3(-3cos(1\u03c0(3((1x - 2)/(1x + 3))^2 + 5((1x - 2)/(1x + 3)) + 2) - 1) - 2) - 2)) - 3) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1((-3(-1(2|(2|(2|x + 1| - 3) - 1| - 1) - 1|)^2 - 3(2|(2|(2|x + 1| - 3) - 1| - 1) - 1|) + 1) - 1)/(2(-1(2|(2|(2|x + 1| - 3) - 1| - 1) - 1|)^2 - 3(2|(2|(2|x + 1| - 3) - 1| - 1) - 1|) + 1) + 3)) + 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3((1((1(5(1|(-2sin(1\u03c0x - 1) + 3) - 2| - 1)))/(-2(5(1|(-2sin(1\u03c0x - 1) + 3) - 2| - 1)) + 3)) - 2)/(2((1(5(1|(-2sin(1\u03c0x - 1) + 3) - 2| - 1)))/(-2(5(1|(-2sin(1\u03c0x - 1) + 3) - 2| - 1)) + 3)) + 2)) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(4(-1sin(2\u03c0((1(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) - 2)/(2(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) + 1)) - 1) - 2)^2 - 4(-1sin(2\u03c0((1(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) - 2)/(2(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) + 1)) - 1) - 2) + 1) + 1)/(-3(4(-1sin(2\u03c0((1(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) - 2)/(2(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) + 1)) - 1) - 2)^2 - 4(-1sin(2\u03c0((1(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) - 2)/(2(2(-1x^2 - 2x + 5)^2 - 5(-1x^2 - 2x + 5) - 2) + 1)) - 1) - 2) + 1) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1((-2((3((3(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) - 3)/(-1(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) + 3)) - 2)/(-1((3(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) - 3)/(-1(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) + 3)) - 3)) + 3)/(-1((3((3(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) - 3)/(-1(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) + 3)) - 2)/(-1((3(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) - 3)/(-1(1sin(2\u03c0(1x^2 - 2x + 4) + 1) - 3) + 3)) - 3)))) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(-1|(-3|((2((-3(2sin(3\u03c0x - 2)) + 1)/(-1(2sin(3\u03c0x - 2)) - 1)) - 3)/(-2((-3(2sin(3\u03c0x - 2)) + 1)/(-1(2sin(3\u03c0x - 2)) - 1)))) + 2| + 2) - 2| + 3) + 1)/(2(-1|(-3|((2((-3(2sin(3\u03c0x - 2)) + 1)/(-1(2sin(3\u03c0x - 2)) - 1)) - 3)/(-2((-3(2sin(3\u03c0x - 2)) + 1)/(-1(2sin(3\u03c0x - 2)) - 1)))) + 2| + 2) - 2| + 3) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(-3cos(1\u03c0(4(-2|(1|(-4x^2 - 1x + 1) - 2| - 3) - 1| + 3)^2 - 2(-2|(1|(-4x^2 - 1x + 1) - 2| - 3) - 1| + 3) - 2) + 1)) + 5 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -5(2|((3(1(-3sin(2\u03c0(2x - 4) - 3)) - 3) + 1)/(-1(1(-3sin(2\u03c0(2x - 4) - 3)) - 3) + 3)) + 3| + 3) - 2 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1sin(2\u03c0(-5((1(2|(-5((-3x + 1)/(-1x + 3)) - 4)| + 3) + 2)/(-3(2|(-5((-3x + 1)/(-1x + 3)) - 4)| + 3) - 1))^2 + 4((1(2|(-5((-3x + 1)/(-1x + 3)) - 4)| + 3) + 2)/(-3(2|(-5((-3x + 1)/(-1x + 3)) - 4)| + 3) - 1)) + 4) + 2) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((2(4(-3sin(2\u03c0(1|(-1x - 3) + 2| + 3) + 1) - 2) - 3) + 1)/(2(4(-3sin(2\u03c0(1|(-1x - 3) + 2| + 3) + 1) - 2) - 3) - 1)) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2((3(2|(-3(3|(-1cos(1\u03c0x) - 1) - 2| + 3) + 4) - 1| - 2) + 1)/(-3(2|(-3(3|(-1cos(1\u03c0x) - 1) - 2| + 3) + 4) - 1| - 2) - 2)))/(1((3(2|(-3(3|(-1cos(1\u03c0x) - 1) - 2| + 3) + 4) - 1| - 2) + 1)/(-3(2|(-3(3|(-1cos(1\u03c0x) - 1) - 2| + 3) + 4) - 1| - 2) - 2)) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2sin(1\u03c0(1|(3|(-2(2|(3x + 4) - 1| - 3) + 1) + 1| + 1) + 1| - 2) + 3) - 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(1((-2(-2|(2sin(2\u03c0(4x^2 - 4x)) - 2) + 2| - 2) - 2)/(2(-2|(2sin(2\u03c0(4x^2 - 4x)) - 2) + 2| - 2) - 1))^2 - 5((-2(-2|(2sin(2\u03c0(4x^2 - 4x)) - 2) + 2| - 2) - 2)/(2(-2|(2sin(2\u03c0(4x^2 - 4x)) - 2) + 2| - 2) - 1)) - 4) + 1| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1|((1(-1(-4(-3cos(2\u03c0x - 3) - 2)^2 + 3(-3cos(2\u03c0x - 3) - 2) + 1)) + 1)/(-2(-1(-4(-3cos(2\u03c0x - 3) - 2)^2 + 3(-3cos(2\u03c0x - 3) - 2) + 1)) - 3)) + 1| - 3)^2 + 2(1|((1(-1(-4(-3cos(2\u03c0x - 3) - 2)^2 + 3(-3cos(2\u03c0x - 3) - 2) + 1)) + 1)/(-2(-1(-4(-3cos(2\u03c0x - 3) - 2)^2 + 3(-3cos(2\u03c0x - 3) - 2) + 1)) - 3)) + 1| - 3) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2(-1sin(3\u03c0(5(-3(-3|((2x - 2)/(2x + 3)) + 2| - 2) - 2)^2 - 3(-3(-3|((2x - 2)/(2x + 3)) + 2| - 2) - 2) - 2) - 1) - 2)^2 + 2(-1sin(3\u03c0(5(-3(-3|((2x - 2)/(2x + 3)) + 2| - 2) - 2)^2 - 3(-3(-3|((2x - 2)/(2x + 3)) + 2| - 2) - 2) - 2) - 1) - 2) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1|(-3(-2(-3((2x + 2)/(-1x - 3))^2 - 4((2x + 2)/(-1x - 3)) + 1) + 3) - 1) - 1|)^2 - 3(-1|(-3(-2(-3((2x + 2)/(-1x - 3))^2 - 4((2x + 2)/(-1x - 3)) + 1) + 3) - 1) - 1|) - 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|((-3(-1(-5(5(-1|x + 2| + 2) + 3)^2 - 5(5(-1|x + 2| + 2) + 3) + 1)^2 + 3(-5(5(-1|x + 2| + 2) + 3)^2 - 5(5(-1|x + 2| + 2) + 3) + 1) + 1) + 2)/(-1(-1(-5(5(-1|x + 2| + 2) + 3)^2 - 5(5(-1|x + 2| + 2) + 3) + 1)^2 + 3(-5(5(-1|x + 2| + 2) + 3)^2 - 5(5(-1|x + 2| + 2) + 3) + 1) + 1)))| + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(3((2(3|(1(1cos(1\u03c0x + 1) + 1) - 2) - 1| + 1) + 1)/(1(3|(1(1cos(1\u03c0x + 1) + 1) - 2) - 1| + 1))) - 5) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(1\u03c0(3(3(-1(-1(-1|x - 3| - 2)^2 + 4(-1|x - 3| - 2) - 1) - 3) - 3) - 4) - 2) - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1sin(3\u03c0(2|(3(-3|(-3(4x^2 - 2x - 3) - 1) - 2| + 3) - 1) + 3| + 2) - 2) + 1, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(1(-2|(-3|(-1cos(1\u03c0(1|x| - 1) - 2) + 1) + 2| - 2) + 2|)^2 - 5(-2|(-3|(-1cos(1\u03c0(1|x| - 1) - 2) + 1) + 2| - 2) + 2|) - 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4((2(-2cos(3\u03c0(-1|(1|(-2x + 5) + 1| + 3) - 2| - 3) + 1) + 1) + 2)/(-2(-2cos(3\u03c0(-1|(1|(-2x + 5) + 1| + 3) - 2| - 3) + 1) + 1) + 3)) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|((-2((3((-1(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 2)/(-3(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 1)) + 1)/(-1((-1(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 2)/(-3(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 1)) + 2)) + 3)/(2((3((-1(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 2)/(-3(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 1)) + 1)/(-1((-1(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 2)/(-3(-2sin(2\u03c0(5x^2 - 1x + 1) - 3)) + 1)) + 2)) - 1)) + 2| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2cos(2\u03c0(-3|(2|((1(1(5x^2 + 3x - 4)^2 - 1(5x^2 + 3x - 4)) + 2)/(2(1(5x^2 + 3x - 4)^2 - 1(5x^2 + 3x - 4)) - 3)) - 2| + 1) + 3| + 2) + 2) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 4(2sin(2\u03c0(1(-1(1(-2|x + 3| - 2) + 3)^2 + 5(1(-2|x + 3| - 2) + 3) + 4) + 2) + 2) - 3) - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1(-1sin(2\u03c0(4(2(1(1x^2 - 4x + 4) + 1)^2 - 3(1(1x^2 - 4x + 4) + 1) - 2)^2 - 5(2(1(1x^2 - 4x + 4) + 1)^2 - 3(1(1x^2 - 4x + 4) + 1) - 2) + 5) - 3) + 1)^2 + 2(-1sin(2\u03c0(4(2(1(1x^2 - 4x + 4) + 1)^2 - 3(1(1x^2 - 4x + 4) + 1) - 2)^2 - 5(2(1(1x^2 - 4x + 4) + 1)^2 - 3(1(1x^2 - 4x + 4) + 1) - 2) + 5) - 3) + 1) - 4 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(3cos(1\u03c0(-1(2|(-1|(2|x + 3| - 2) + 1|) - 3| + 1) + 5) + 1) + 2)^2 - 1(3cos(1\u03c0(-1(2|(-1|(2|x + 3| - 2) + 1|) - 3| + 1) + 5) + 1) + 2) - 3, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 2(-1(-1(-1|(-3|(-3sin(2\u03c0x - 1) - 3) + 2| - 2)| + 2) - 4) - 5) + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-5(-4(5(-3|(-2|x - 2|) + 1| + 2) - 5)^2 + 3(5(-3|(-2|x - 2|) + 1| + 2) - 5) + 1)^2 - 5) - 1)/(-3(-5(-4(5(-3|(-2|x - 2|) + 1| + 2) - 5)^2 + 3(5(-3|(-2|x - 2|) + 1| + 2) - 5) + 1)^2 - 5) + 4) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -3(-5((-3(1cos(1\u03c0(-3(-3|x - 1| + 1)) - 3)) - 1)/(-1(1cos(1\u03c0(-3(-3|x - 1| + 1)) - 3)) + 3))^2 - 2((-3(1cos(1\u03c0(-3(-3|x - 1| + 1)) - 3)) - 1)/(-1(1cos(1\u03c0(-3(-3|x - 1| + 1)) - 3)) + 3)) - 1) + 3, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(1cos(2\u03c0(-3(-1|(-4((1x)/(-3x - 2))^2 - 4((1x)/(-3x - 2)) + 5) - 2| + 1)^2 - 5) + 3) - 2)^2 + 5(1cos(2\u03c0(-3(-1|(-4((1x)/(-3x - 2))^2 - 4((1x)/(-3x - 2)) + 5) - 2| + 1)^2 - 5) + 3) - 2) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(3\u03c0((-2(-1|(2|(1(1|x + 3| - 1)^2 + 2(1|x + 3| - 1) - 5) - 2| - 1) + 2| - 2) - 3)/(-2(-1|(2|(1(1|x + 3| - 1)^2 + 2(1|x + 3| - 1) - 5) - 2| - 1) + 2| - 2) - 1)) - 1) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3|(3|(-3(-2|(2sin(2\u03c0(-1x - 4) + 2) + 1) + 2| - 3) - 4) + 1| - 3) + 3| + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1(3((2((1(3|(1x^2 - 4x - 1) + 3| - 3) + 2)/(-3(3|(1x^2 - 4x - 1) + 3| - 3) - 1)) - 1)/(-2((1(3|(1x^2 - 4x - 1) + 3| - 3) + 2)/(-3(3|(1x^2 - 4x - 1) + 3| - 3) - 1)) + 3))^2 + 1((2((1(3|(1x^2 - 4x - 1) + 3| - 3) + 2)/(-3(3|(1x^2 - 4x - 1) + 3| - 3) - 1)) - 1)/(-2((1(3|(1x^2 - 4x - 1) + 3| - 3) + 2)/(-3(3|(1x^2 - 4x - 1) + 3| - 3) - 1)) + 3)) - 5) + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(3|(-3(3cos(3\u03c0((3((1x + 2)/(1x - 2)) - 3)/(2((1x + 2)/(1x - 2)) - 1))) - 3))| - 2) + 3| + 3 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(4(-1(1|(4(-3cos(2\u03c0x) - 1) + 4) + 2| - 3)^2 - 2(1|(4(-3cos(2\u03c0x) - 1) + 4) + 2| - 3) - 5) + 4) + 2| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 2(4((1(-2sin(1\u03c0(1|(2|x - 1| + 2) + 1| + 1) + 2) + 1) - 3)/(2(-2sin(1\u03c0(1|(2|x - 1| + 2) + 1| + 1) + 2) + 1) - 3)) - 4)^2 - 1(4((1(-2sin(1\u03c0(1|(2|x - 1| + 2) + 1| + 1) + 2) + 1) - 3)/(2(-2sin(1\u03c0(1|(2|x - 1| + 2) + 1| + 1) + 2) + 1) - 3)) - 4) - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-5(1(2cos(1\u03c0(1|(-1x^2 - 1x - 4) - 3| - 1) - 3) + 2)^2 - 5(2cos(1\u03c0(1|(-1x^2 - 1x - 4) - 3| - 1) - 3) + 2) - 2) + 2) - 2| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2cos(2\u03c0((-2(-3|(-4((3(3|x - 2| - 2) - 3)/(3(3|x - 2| - 2) + 3)) - 1) + 3| + 1))/(2(-3|(-4((3(3|x - 2| - 2) - 3)/(3(3|x - 2| - 2) + 3)) - 1) + 3| + 1) - 3)) + 1) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1sin(2\u03c0((-2(1(-3((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1))^2 - 2((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1)) - 3)^2 + 5(-3((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1))^2 - 2((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1)) - 3) + 1) + 2)/(-1(1(-3((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1))^2 - 2((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1)) - 3)^2 + 5(-3((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1))^2 - 2((1(-5x^2 + 4x - 5) - 3)/(3(-5x^2 + 4x - 5) - 1)) - 3) + 1) - 1)) - 3) + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -4(1(-1sin(1\u03c0(1(-3|(2|x - 3|) + 3| + 3)^2 + 2(-3|(2|x - 3|) + 3| + 3) - 1) + 2)) - 3) - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(5(-3(1(-4(-1|x| + 2)^2 + 2(-1|x| + 2) + 5) + 3) + 5)^2 + 1(-3(1(-4(-1|x| + 2)^2 + 2(-1|x| + 2) + 5) + 3) + 5) + 3) + 3)/(-3(5(-3(1(-4(-1|x| + 2)^2 + 2(-1|x| + 2) + 5) + 3) + 5)^2 + 1(-3(1(-4(-1|x| + 2)^2 + 2(-1|x| + 2) + 5) + 3) + 5) + 3) + 4) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1|(2cos(1\u03c0(2(-5((-3(-1|x - 3|) - 3)/(-1(-1|x - 3|) + 2)) - 4) - 2)) - 1) + 3| - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 1|(1(1|(-2sin(3\u03c0(-3(4x^2 - 4x - 5) + 1) + 1) + 2) - 1| - 2) - 1) - 1| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -4(-4(1|(3(1cos(3\u03c0(2x)))^2 - 5(1cos(3\u03c0(2x))) + 2) - 1| + 3)^2 - 5(1|(3(1cos(3\u03c0(2x)))^2 - 5(1cos(3\u03c0(2x))) + 2) - 1| + 3)) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -4(-1(-3|(1|(3(1sin(3\u03c0x) - 2)^2 + 1(1sin(3\u03c0x) - 2) + 3) + 3| - 1) - 2|)) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1((-3(5(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2)^2 - 3(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2) + 1))/(-1(5(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2)^2 - 3(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2) + 1) - 3))^2 - 4((-3(5(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2)^2 - 3(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2) + 1))/(-1(5(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2)^2 - 3(-1sin(3\u03c0(4(5x + 1) - 3) + 2) + 2) + 1) - 3)) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2(5(-2sin(3\u03c0((3((-3(1x^2 - 4x - 4) + 2)/(1(1x^2 - 4x - 4))))/(-2((-3(1x^2 - 4x - 4) + 2)/(1(1x^2 - 4x - 4))) - 3))))^2 + 5(-2sin(3\u03c0((3((-3(1x^2 - 4x - 4) + 2)/(1(1x^2 - 4x - 4))))/(-2((-3(1x^2 - 4x - 4) + 2)/(1(1x^2 - 4x - 4))) - 3)))))^2 + 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(-5(2(2((-1(-1x^2 - 5x - 4) - 1)/(-2(-1x^2 - 5x - 4) + 1))^2 + 5((-1(-1x^2 - 5x - 4) - 1)/(-2(-1x^2 - 5x - 4) + 1)) - 4)^2 + 5(2((-1(-1x^2 - 5x - 4) - 1)/(-2(-1x^2 - 5x - 4) + 1))^2 + 5((-1(-1x^2 - 5x - 4) - 1)/(-2(-1x^2 - 5x - 4) + 1)) - 4) - 2) - 1) - 2| - 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2|(3|((2(-3(2(-2sin(2\u03c0x - 1) - 1)^2 + 4(-2sin(2\u03c0x - 1) - 1) + 2) + 3) + 2)/(-3(-3(2(-2sin(2\u03c0x - 1) - 1)^2 + 4(-2sin(2\u03c0x - 1) - 1) + 2) + 3) + 1)) - 1| + 3)| - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4(1((-2(-2cos(1\u03c0(1((3x - 1)/(-1x - 2)) + 2) - 1) - 2))/(-1(-2cos(1\u03c0(1((3x - 1)/(-1x - 2)) + 2) - 1) - 2) + 2)) + 4) - 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2((3(2(-3(-1sin(1\u03c0(-2x + 3) + 1) + 1)) - 5) - 2)/(2(2(-3(-1sin(1\u03c0(-2x + 3) + 1) + 1)) - 5))))/(-2((3(2(-3(-1sin(1\u03c0(-2x + 3) + 1) + 1)) - 5) - 2)/(2(2(-3(-1sin(1\u03c0(-2x + 3) + 1) + 1)) - 5))) - 3), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|(-5((-3(-2sin(2\u03c0(4(4x - 4)) + 1) - 2) - 3)/(2(-2sin(2\u03c0(4(4x - 4)) + 1) - 2) - 1)) + 5)| - 1 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (3(5(3((1(-2|(3|x + 1| + 1) - 2| + 3))/(-1(-2|(3|x + 1| + 1) - 2| + 3) + 2))^2 - 2((1(-2|(3|x + 1| + 1) - 2| + 3))/(-1(-2|(3|x + 1| + 1) - 2| + 3) + 2)) + 5) - 2) - 3)/(1(5(3((1(-2|(3|x + 1| + 1) - 2| + 3))/(-1(-2|(3|x + 1| + 1) - 2| + 3) + 2))^2 - 2((1(-2|(3|x + 1| + 1) - 2| + 3))/(-1(-2|(3|x + 1| + 1) - 2| + 3) + 2)) + 5) - 2) + 3) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 5(3|((1(-2sin(2\u03c0(-3|((1x + 3)/(-3x)) + 3| - 2) - 2) + 1) + 2)/(3(-2sin(2\u03c0(-3|((1x + 3)/(-3x)) + 3| - 2) - 2) + 1) + 2)) + 1|) - 5, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3|(-1(-4(1sin(3\u03c0(3|(-5x - 3) + 2| - 2) - 1) - 2) - 3) - 5)| + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -2|(2(1(-2|(-3(-3|x - 2| + 1)^2 - 5(-3|x - 2| + 1) + 5) - 3| + 3)^2 + 4(-2|(-3(-3|x - 2| + 1)^2 - 5(-3|x - 2| + 1) + 5) - 3| + 3) - 3) + 3) - 3| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -2|(-1|((1((2(-1((-1x - 1)/(-2x))^2 - 5((-1x - 1)/(-2x)) - 4) - 2)/(1(-1((-1x - 1)/(-2x))^2 - 5((-1x - 1)/(-2x)) - 4) + 3)) - 3)/(3((2(-1((-1x - 1)/(-2x))^2 - 5((-1x - 1)/(-2x)) - 4) - 2)/(1(-1((-1x - 1)/(-2x))^2 - 5((-1x - 1)/(-2x)) - 4) + 3)) + 1))| - 1) + 2| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(-2(1|(5(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2)^2 + 3(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2) - 4) - 2|)^2 + 5(1|(5(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2)^2 + 3(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2) - 4) - 2|) - 2) + 2)/(-1(-2(1|(5(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2)^2 + 3(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2) - 4) - 2|)^2 + 5(1|(5(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2)^2 + 3(-2sin(1\u03c0(1x^2 - 3x) - 3) + 2) - 4) - 2|) - 2) + 2), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(5((3(-1|(-1sin(1\u03c0(5x - 5)) + 2) - 1| + 2) + 1)/(1(-1|(-1sin(1\u03c0(5x - 5)) + 2) - 1| + 2) - 3))^2 + 2((3(-1|(-1sin(1\u03c0(5x - 5)) + 2) - 1| + 2) + 1)/(1(-1|(-1sin(1\u03c0(5x - 5)) + 2) - 1| + 2) - 3)) + 1) + 3| - 2 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1|(3(3(3sin(2\u03c0(-4((-3x + 1)/(3x + 3)) - 2) - 2) + 2) + 5) - 4) + 3| + 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-3(3cos(1\u03c0(3|(-1(-5x - 5)^2 + 5(-5x - 5)) - 2| - 2) + 1) + 3)^2 - 2(3cos(1\u03c0(3|(-1(-5x - 5)^2 + 5(-5x - 5)) - 2| - 2) + 1) + 3)) + 3)/(3(-3(3cos(1\u03c0(3|(-1(-5x - 5)^2 + 5(-5x - 5)) - 2| - 2) + 1) + 3)^2 - 2(3cos(1\u03c0(3|(-1(-5x - 5)^2 + 5(-5x - 5)) - 2| - 2) + 1) + 3)) + 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -2sin(2\u03c0(4(-2|(-3|(-1((2x + 1)/(-1x + 3)) - 1) - 2| + 3) + 3| + 3) - 4) - 2) + 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(1cos(3\u03c0((-3(-5((3(3|x| - 1) + 3)/(-1(3|x| - 1) - 3))^2 + 5((3(3|x| - 1) + 3)/(-1(3|x| - 1) - 3)) + 4) - 2)/(1(-5((3(3|x| - 1) + 3)/(-1(3|x| - 1) - 3))^2 + 5((3(3|x| - 1) + 3)/(-1(3|x| - 1) - 3)) + 4) + 2)) - 1))| positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (1(-2(-3(-1sin(1\u03c0(4(1x - 3) - 1) - 3) - 1) - 5) - 5))/(3(-2(-3(-1sin(1\u03c0(4(1x - 3) - 1) - 3) - 1) - 5) - 5) - 2) is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -3(-1(-1((-3(1|((1x - 3)/(2x + 3)) - 3| - 3) - 2)/(-2(1|((1x - 3)/(2x + 3)) - 3| - 3) + 3)) + 4)^2 + 2(-1((-3(1|((1x - 3)/(2x + 3)) - 3| - 3) - 2)/(-2(1|((1x - 3)/(2x + 3)) - 3| - 3) + 3)) + 4) - 1) - 4 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(-3|(4((-1(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 3)/(2(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 2))^2 - 5((-1(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 3)/(2(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 2)) - 5) - 3| + 2) + 1)/(3(-3|(4((-1(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 3)/(2(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 2))^2 - 5((-1(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 3)/(2(2|((2x + 2)/(-1x + 2)) - 1| - 3) + 2)) - 5) - 3| + 2) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-3cos(1\u03c0(4((1((2(-4x + 1))/(-1(-4x + 1) - 3)) + 1)/(1((2(-4x + 1))/(-1(-4x + 1) - 3)) + 3)) - 1)) + 2) - 5 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1(-1|(4(2cos(3\u03c0((-3(1x - 3) - 3)/(-3(1x - 3) - 2)) - 1) + 1) - 1) - 1| - 3) - 4 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1|(-2|(-2|(1(-3sin(3\u03c0((-2x + 2)/(-3x + 1))) - 2)^2 - 5(-3sin(3\u03c0((-2x + 2)/(-3x + 1))) - 2) + 2) + 2| - 1) + 3| - 1) + 3| - 1 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(4((1(3|(-1cos(2\u03c0((2x - 3)/(2x)) + 2) + 1) - 1| - 3) - 1)/(-2(3|(-1cos(2\u03c0((2x - 3)/(2x)) + 2) + 1) - 1| - 3) - 3)) + 3))/(2(4((1(3|(-1cos(2\u03c0((2x - 3)/(2x)) + 2) + 1) - 1| - 3) - 1)/(-2(3|(-1cos(2\u03c0((2x - 3)/(2x)) + 2) + 1) - 1| - 3) - 3)) + 3) - 1), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 4((-2(4((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3))^2 - 5((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3)) - 4) + 1)/(-3(4((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3))^2 - 5((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3)) - 4) - 2))^2 - 4((-2(4((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3))^2 - 5((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3)) - 4) + 1)/(-3(4((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3))^2 - 5((2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 1)/(2(3|((3x + 3)/(-1x + 2)) + 2| - 1) - 3)) - 4) - 2)) - 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = -1cos(1\u03c0(2|(3|(-2|(-5((1x)/(-3x + 2)) - 5) + 2| + 3) - 1| + 3) - 3| - 3) - 3) - 2, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 5(-4((3(4(-5(1cos(1\u03c0x) + 3) + 1)^2 - 3(-5(1cos(1\u03c0x) + 3) + 1) + 3) + 3)/(-3(4(-5(1cos(1\u03c0x) + 3) + 1)^2 - 3(-5(1cos(1\u03c0x) + 3) + 1) + 3) - 1))^2 + 2((3(4(-5(1cos(1\u03c0x) + 3) + 1)^2 - 3(-5(1cos(1\u03c0x) + 3) + 1) + 3) + 3)/(-3(4(-5(1cos(1\u03c0x) + 3) + 1)^2 - 3(-5(1cos(1\u03c0x) + 3) + 1) + 3) - 1)) + 4)^2 + 3 positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 1cos(2\u03c0((1(3|(3(3|((-2x - 2)/(3x - 2)) + 2| - 1)^2 - 1(3|((-2x - 2)/(3x - 2)) + 2| - 1) + 2) + 2| - 2))/(3(3|(3(3|((-2x - 2)/(3x - 2)) + 2| - 1)^2 - 1(3|((-2x - 2)/(3x - 2)) + 2| - 1) + 2) + 2| - 2) - 1)) + 1) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-3cos(1\u03c0(-3(1|(-2|(-5x - 1) + 1| + 1) - 1| + 1) + 1) - 3) + 2)^2 - 1(-3cos(1\u03c0(-3(1|(-2|(-5x - 1) + 1| + 1) - 1| + 1) + 1) - 3) + 2) + 2 is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = 1(2((2((-1(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)/(3(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)) + 1)/(1((-1(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)/(3(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)))) - 3)^2 - 2(2((2((-1(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)/(3(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)) + 1)/(1((-1(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)/(3(3(-2cos(2\u03c0x + 2) - 1) - 2) - 1)))) - 3) - 1, find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = -1|((1(1sin(2\u03c0(3(5(-3x^2 + 4x + 1) + 2) - 3)) - 3) + 1)/(-2(1sin(2\u03c0(3(5(-3x^2 + 4x + 1) + 2) - 3)) - 3) + 1)) - 1| - 3 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (-1(2((-1((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) - 3)/(2((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) + 1))^2 - 4((-1((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) - 3)/(2((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) + 1)) - 5) - 3)/(2(2((-1((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) - 3)/(2((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) + 1))^2 - 4((-1((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) - 3)/(2((3(-2|(5x^2 - 5x - 2)| + 3) + 2)/(-3(-2|(5x^2 - 5x - 2)| + 3) + 4)) + 1)) - 5) + 3), find the number of maximal connected intervals in [-10, 10] where f'(x) < 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-3(-3cos(3\u03c0(-1((3(2(3x^2 + 4x - 3)^2 - 5) - 3)/(-1(2(3x^2 + 4x - 3)^2 - 5) - 3))^2 + 4((3(2(3x^2 + 4x - 3)^2 - 5) - 3)/(-1(2(3x^2 + 4x - 3)^2 - 5) - 3)) + 5) - 3) - 1) + 2)/(2(-3cos(3\u03c0(-1((3(2(3x^2 + 4x - 3)^2 - 5) - 3)/(-1(2(3x^2 + 4x - 3)^2 - 5) - 3))^2 + 4((3(2(3x^2 + 4x - 3)^2 - 5) - 3)/(-1(2(3x^2 + 4x - 3)^2 - 5) - 3)) + 5) - 3) - 1) + 2) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "For the function f(x) = (2(-2(2cos(3\u03c0((3(-2|(-5x^2 - 2x + 4)| - 1) + 2)/(2(-2|(-5x^2 - 2x + 4)| - 1) + 3)) - 3) + 3) - 5) - 3)/(3(-2(2cos(3\u03c0((3(-2|(-5x^2 - 2x + 4)| - 1) + 2)/(2(-2|(-5x^2 - 2x + 4)| - 1) + 3)) - 3) + 3) - 5) - 2), find the number of maximal connected intervals in [-10, 10] where f'(x) > 0.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = 3|(-1cos(3\u03c0(-2|(-2|((3(-2|x - 1| - 2) - 2)/(-2(-2|x - 1| - 2))) - 1| + 3)| + 3) + 1) - 2) + 1| + 2 negative?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -3((-3(1cos(2\u03c0(1|(-2(3x^2 - 2x - 2)^2 - 2(3x^2 - 2x - 2) - 5) + 1| + 2) + 3)) - 2)/(-1(1cos(2\u03c0(1|(-2(3x^2 - 2x - 2)^2 - 2(3x^2 - 2x - 2) - 5) + 1| + 2) + 3)) - 1)) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = 2|(3|((1(3sin(1\u03c0(-5(2x^2 + 5x - 5) - 4) + 1) - 3) - 1)/(3(3sin(1\u03c0(-5(2x^2 + 5x - 5) - 4) + 1) - 3) + 2)) - 3| - 1) + 3| is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(2|(-3|(-3|((1((-2x + 1)/(-3x - 3)) + 1)/(1((-2x + 1)/(-3x - 3)))) - 3| + 1) + 1|) + 2|) + 1 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = -1(-1(-2(-1(-2|(-5x) - 1|)^2 - 4(-2|(-5x) - 1|) - 3)^2 + 3) + 3) - 3 is strictly increasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "On how many maximal connected intervals within [-10, 10] is the derivative of f(x) = (-1(-3cos(2\u03c0(-5((-1(-2|((2x)/(-2x - 2)) - 3| - 3) - 1)/(1(-2|((2x)/(-2x - 2)) - 3| - 3)))^2 + 5((-1(-2|((2x)/(-2x - 2)) - 3| - 3) - 1)/(1(-2|((2x)/(-2x - 2)) - 3| - 3))) - 5) - 1) - 2) - 1)/(-1(-3cos(2\u03c0(-5((-1(-2|((2x)/(-2x - 2)) - 3| - 3) - 1)/(1(-2|((2x)/(-2x - 2)) - 3| - 3)))^2 + 5((-1(-2|((2x)/(-2x - 2)) - 3| - 3) - 1)/(1(-2|((2x)/(-2x - 2)) - 3| - 3))) - 5) - 1) - 2)) positive?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (2(5(3sin(1\u03c0(1(1|((-2x - 2)/(-1x + 3)) - 2| - 3)^2 + 4(1|((-2x - 2)/(-1x + 3)) - 2| - 3) - 2) + 1) - 2) - 1) + 3)/(3(5(3sin(1\u03c0(1(1|((-2x - 2)/(-1x + 3)) - 2| - 3)^2 + 4(1|((-2x - 2)/(-1x + 3)) - 2| - 3) - 2) + 1) - 2) - 1) - 1) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of maximal connected intervals in [-10, 10] where the function f(x) = (-2(3|(-1|(1|(-3|(2|x + 1| - 1) - 3| + 2) - 1| - 3) - 1| - 3) - 1|) + 3)/(-1(3|(-1|(1|(-3|(2|x + 1| - 1) - 3| + 2) - 1| - 3) - 1| - 3) - 1|)) is strictly decreasing.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}