{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(2sin(3\u03c0(-3(3|x - 3| - 1)^2 - 5(3|x - 3| - 1) + 2) - 1) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1116", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(2sin(3\u03c0(-2|(-2x^2 - 1x - 3) + 3| + 2) - 3)) + 2)/(2(2sin(3\u03c0(-2|(-2x^2 - 1x - 3) + 3| + 2) - 3)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1022", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(3cos(2\u03c0((-2(-5x^2 - 2x + 2) - 3)/(-2(-5x^2 - 2x + 2) + 1)) + 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-3(-3|(-1sin(1\u03c0x - 2) + 2) - 1| + 1)^2 + 2) - 2)/(1(-3(-3|(-1sin(1\u03c0x - 2) + 2) - 1| + 1)^2 + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0((1(-5x + 1) - 3)/(-2(-5x + 1) + 3)) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((3(2sin(1\u03c0x + 2) - 1) + 2)/(2(2sin(1\u03c0x + 2) - 1) - 1)) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(5((-3(3|x| - 3) - 3)/(-1(3|x| - 3)))^2 - 1((-3(3|x| - 3) - 3)/(-1(3|x| - 3)))) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1cos(2\u03c0(5x + 2) + 2) - 2) - 1)/(3(1cos(2\u03c0(5x + 2) + 2) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-1cos(1\u03c0((-1(3x^2 - 4x - 1) + 2)/(2(3x^2 - 4x - 1) - 1)) + 2) - 2) + 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|((-1(1sin(1\u03c0(-1x - 2) + 2) - 1) + 3)/(-2(1sin(1\u03c0(-1x - 2) + 2) - 1) - 1)) - 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(2\u03c0(2|((1(2x - 5) + 1)/(3(2x - 5) - 1)) + 3| + 2) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(3(2sin(1\u03c0(2|x + 3| + 3) - 3))^2 - 3))/(-1(3(2sin(1\u03c0(2|x + 3| + 3) - 3))^2 - 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(2cos(1\u03c0(1(-2x - 4)^2 + 4(-2x - 4)) - 3) + 1) + 2)/(1(2cos(1\u03c0(1(-2x - 4)^2 + 4(-2x - 4)) - 3) + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "513", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-2|(2cos(2\u03c0(5x + 4) - 1) - 3) + 1|))/(3(-2|(2cos(2\u03c0(5x + 4) - 1) - 3) + 1|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(2cos(1\u03c0(1x - 4) - 1) + 3) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-1(-4(-1cos(3\u03c0x + 3))^2 + 5(-1cos(3\u03c0x + 3)) + 3) + 1) + 1)/(1(-1(-4(-1cos(3\u03c0x + 3))^2 + 5(-1cos(3\u03c0x + 3)) + 3) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-2sin(1\u03c0(2|x - 1| + 1) - 2) + 2))/(2(-2sin(1\u03c0(2|x - 1| + 1) - 2) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-1|((-2(-1x^2 - 4x) + 2)/(1(-1x^2 - 4x) + 2)) + 1| + 2) + 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(1sin(3\u03c0(3x^2 - 2x + 3) + 3)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1375", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(4(-1sin(1\u03c0x + 2)))^2 + 2(4(-1sin(1\u03c0x + 2))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-5(2sin(2\u03c0(-1|x - 3| + 2) - 3) + 2)^2 - 1(2sin(2\u03c0(-1|x - 3| + 2) - 3) + 2) + 3) + 3)/(2(-5(2sin(2\u03c0(-1|x - 3| + 2) - 3) + 2)^2 - 1(2sin(2\u03c0(-1|x - 3| + 2) - 3) + 2) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(-3(5(-2|x - 3|)^2 + 3) + 5)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1421", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2cos(2\u03c0(3(-2|x - 2| - 3) - 3) - 3) + 1)^2 - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(1\u03c0(-1|((-1(-5x^2 + 3x + 4))/(-3(-5x^2 + 3x + 4) + 4)) - 1| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0(4((3(3x - 4) - 3)/(-2(3x - 4) - 1))^2 - 5((3(3x - 4) - 3)/(-2(3x - 4) - 1)) - 2) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(5(2sin(3\u03c0((-2x - 1)/(2x - 3)) + 1) - 2)) - 1| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0((-3(2|x + 2| - 3) + 3)/(2(2|x + 2| - 3) + 3)) - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(3sin(2\u03c0(5(3|x| + 2) - 1) - 2) + 1) + 1)/(-3(3sin(2\u03c0(5(3|x| + 2) - 1) - 2) + 1) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(3\u03c0(-2|(3((3x + 1)/(2x - 3))) - 3| - 2) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|((3(-3(3sin(2\u03c0x) - 1)^2 + 1(3sin(2\u03c0x) - 1)) + 3)/(-2(-3(3sin(2\u03c0x) - 1)^2 + 1(3sin(2\u03c0x) - 1)) + 3))| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "43", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(3(-1|(-2x^2 - 2x - 1) - 3| - 3) + 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1615", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2sin(3\u03c0(5x^2 + 2x - 5)) - 3) - 1)/(-3(2sin(3\u03c0(5x^2 + 2x - 5)) - 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1100", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3|(-3cos(2\u03c0((3x + 1)/(2x - 1)) - 3) - 2) + 2| - 2)^2 - 5(3|(-3cos(2\u03c0((3x + 1)/(2x - 1)) - 3) - 2) + 2| - 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(3sin(3\u03c0((2x - 2)/(-2x + 3)) - 3) + 2) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(-1|(-1x^2 + 5x + 2)| - 2) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1cos(3\u03c0(3(1|x - 1| - 2) - 3) + 1))^2 + 4(-1cos(3\u03c0(3(1|x - 1| - 2) - 3) + 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(3\u03c0(2|((-2(-1x - 5) + 3)/(-1(-1x - 5) + 3)) - 2|) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0((-2(1x + 3) - 1)/(-1(1x + 3) - 3)) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3cos(2\u03c0(-5(1x + 2)^2 + 4(1x + 2) - 5) + 1) + 2))/(-2(3cos(2\u03c0(-5(1x + 2)^2 + 4(1x + 2) - 5) + 1) + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "770", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3cos(3\u03c0(1x^2 + 5x - 5) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-1sin(3\u03c0(-3((2x - 1)/(-1x - 3)) + 2) - 3)) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "284", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(1(3cos(2\u03c0x - 2) + 1)^2 - 1(3cos(2\u03c0x - 2) + 1) + 2) + 2)/(-2(1(3cos(2\u03c0x - 2) + 1)^2 - 1(3cos(2\u03c0x - 2) + 1) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(2(-5x + 1)^2 + 3(-5x + 1) + 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1579", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(3(1x + 2)^2 + 2(1x + 2) + 1) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "789", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(2sin(2\u03c0(1((2x + 3)/(-3x + 2)) - 2) + 1) - 2)^2 + 2(2sin(2\u03c0(1((2x + 3)/(-3x + 2)) - 2) + 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2(5(-2sin(3\u03c0x + 1) - 1)^2 + 2(-2sin(3\u03c0x + 1) - 1) - 2) + 2) + 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-3sin(1\u03c0(-2|x + 3| - 1) + 2) + 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-3sin(2\u03c0((1(1x^2 + 4x + 1) + 3)/(1(1x^2 + 4x + 1) - 3)) + 1) + 3) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3cos(3\u03c0(-3x) - 2) - 1))/(-1(3cos(3\u03c0(-3x) - 2) - 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3cos(3\u03c0(-3|x - 1| + 2) + 3))^2 - 1(-3cos(3\u03c0(-3|x - 1| + 2) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0((-1(-4(-2x^2 + 4x + 4)))/(-2(-4(-2x^2 + 4x + 4)) - 3)) + 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-3sin(1\u03c0(-2|x + 1| + 1)) + 3))/(-1(-3sin(1\u03c0(-2|x + 1| + 1)) + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(3cos(1\u03c0((2x + 1)/(-1x + 2)) - 3) - 2) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0(2(3|x + 2| + 1) - 3) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "359", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-3(-1cos(1\u03c0(-1x) - 2) - 2)^2 - 3(-1cos(1\u03c0(-1x) - 2) - 2) + 3) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(1(-1sin(2\u03c0x - 1) + 3)^2 - 2(-1sin(2\u03c0x - 1) + 3) - 3) + 1)/(-1(1(-1sin(2\u03c0x - 1) + 3)^2 - 2(-1sin(2\u03c0x - 1) + 3) - 3) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1(-1sin(2\u03c0(2|x - 2| - 1) + 2) - 1) - 2) - 3)/(-2(1(-1sin(2\u03c0(2|x - 2| - 1) + 2) - 1) - 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2(-3sin(2\u03c0((-1x - 2)/(2x + 3)) + 1) - 1) - 5)^2 + 2(2(-3sin(2\u03c0((-1x - 2)/(2x + 3)) + 1) - 1) - 5) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-2sin(3\u03c0(1|x - 2| - 3) + 1) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3sin(2\u03c0((-1x + 2)/(-3x - 2)) - 1) - 1)^2 - 1(-3sin(2\u03c0((-1x + 2)/(-3x - 2)) - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|((3(1(-3sin(2\u03c0x + 2) - 2)^2 - 5(-3sin(2\u03c0x + 2) - 2) - 4) + 2)/(-3(1(-3sin(2\u03c0x + 2) - 2)^2 - 5(-3sin(2\u03c0x + 2) - 2) - 4) + 2)) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(1|(3cos(1\u03c0x - 2) + 1) + 1| + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-4(-1cos(3\u03c0(1x - 3) + 1) + 1)^2 - 1(-1cos(3\u03c0(1x - 3) + 1) + 1) + 1) - 2)/(3(-4(-1cos(3\u03c0(1x - 3) + 1) + 1)^2 - 1(-1cos(3\u03c0(1x - 3) + 1) + 1) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1\u03c0(1((-1x + 2)/(1x - 3)) - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2sin(1\u03c0((-3(3x^2 + 5x - 5) - 1)/(2(3x^2 + 5x - 5))) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(3((3(2sin(1\u03c0x + 2) + 2) + 3)/(3(2sin(1\u03c0x + 2) + 2) - 2)) - 4)^2 + 3(3((3(2sin(1\u03c0x + 2) + 2) + 3)/(3(2sin(1\u03c0x + 2) + 2) - 2)) - 4) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(2\u03c0((-1(1x - 4) - 2)/(-2(1x - 4) - 1)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-2cos(3\u03c0(1x^2 + 2x + 5) - 2) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "274", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(3|(-2sin(2\u03c0x + 3) + 2)|)^2 + 3(3|(-2sin(2\u03c0x + 3) + 2)|) + 2) - 2)/(-2(-2(3|(-2sin(2\u03c0x + 3) + 2)|)^2 + 3(3|(-2sin(2\u03c0x + 3) + 2)|) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3sin(3\u03c0(4(-3|x - 3| + 2) - 1) - 2))^2 - 4(-3sin(3\u03c0(4(-3|x - 3| + 2) - 1) - 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0((-3(2x^2 + 5x + 2) - 3)/(3(2x^2 + 5x + 2) - 2)) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0(-1|(-4x^2 + 1x + 4) - 2| + 1) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "973", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(5(1|(-2sin(1\u03c0x - 2) + 1) - 2| - 3)^2 - 3(1|(-2sin(1\u03c0x - 2) + 1) - 2| - 3) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(-1((-1x + 1)/(1x + 1))^2 + 5((-1x + 1)/(1x + 1)) + 4) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(1cos(3\u03c0(5(-1x + 4)^2 - 2(-1x + 4)) + 3) + 3) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1050", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(1|(-3cos(3\u03c0x + 3) - 1) - 2| - 2) - 1)/(1(1|(-3cos(3\u03c0x + 3) - 1) - 2| - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(-3|(-1(1x^2 + 5x - 3) - 4)|) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-1(2|x - 3| + 3)^2 + 2(2|x - 3| + 3) - 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1500", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-2|((1x + 2)/(2x + 2)) + 2| + 3) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-2cos(1\u03c0(2|(-1x^2 - 2x + 5) - 1| - 2))) + 3)/(2(-2cos(1\u03c0(2|(-1x^2 - 2x + 5) - 1| - 2))) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "404", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(4(2cos(2\u03c0((1x - 1)/(-2x - 1)) - 2) + 1) + 2)^2 + 4(4(2cos(2\u03c0((1x - 1)/(-2x - 1)) - 2) + 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(4(1cos(3\u03c0x - 2) - 2) + 5) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0((2(-2x^2 - 5x + 2) - 2)/(2(-2x^2 - 5x + 2) + 3)) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(1\u03c0(2((2x + 2)/(-1x + 2)) - 4) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(3(2(-2sin(3\u03c0x + 2) + 2) - 4)^2 - 5(2(-2sin(3\u03c0x + 2) + 2) - 4) - 1) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(-2|(-3((3x + 1)/(-1x - 1))) + 1| - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "181", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3|(3(-3cos(1\u03c0x - 2) - 1)^2 + 2(-3cos(1\u03c0x - 2) - 1) - 2) - 1| - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(2\u03c0(1(3|(4x - 3) + 1| - 2)^2 - 4(3|(4x - 3) + 1| - 2) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1437", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3sin(2\u03c0(-3x^2 - 4x - 3) + 3) + 3) - 1)/(1(3sin(2\u03c0(-3x^2 - 4x - 3) + 3) + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1014", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0(1(-2((3x - 3)/(3x + 2)) - 1)^2 - 2(-2((3x - 3)/(3x + 2)) - 1) + 5) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(5(-1|(3x + 2) + 2| - 3)^2 + 2(-1|(3x + 2) + 2| - 3) - 3) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1428", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-2(-3|((-2x - 2)/(3x + 2)) - 2| + 2) - 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-1sin(1\u03c0(-1|(-1x - 3) - 2| - 3) - 3)) - 1)/(3(-1sin(1\u03c0(-1|(-1x - 3) - 2| - 3) - 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(1|(3sin(1\u03c0x - 3)) - 2| - 2)^2 + 4(1|(3sin(1\u03c0x - 3)) - 2| - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-2cos(3\u03c0(-2(3|x - 3| + 2)) - 3) + 3)^2 + 3(-2cos(3\u03c0(-2(3|x - 3| + 2)) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(4(3sin(1\u03c0((-1x + 1)/(2x)) - 2) + 1)^2 + 4(3sin(1\u03c0((-1x + 1)/(2x)) - 2) + 1) - 1)| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-3e^(-2(3(-2|x| - 1)^2 + 2(-2|x| - 1) - 2)) + 2) - 2)/(-2(-3e^(-2(3(-2|x| - 1)^2 + 2(-2|x| - 1) - 2)) + 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-4(3|(-2cos(1\u03c0x + 3)) - 2| - 2) - 5) + 3)/(3(-4(3|(-2cos(1\u03c0x + 3)) - 2| - 2) - 5) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(3(3sin(1\u03c0(5x^2 - 3x)) - 3) + 2) + 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-1cos(3\u03c0((-2x - 1)/(-1x + 3))) - 2)^2 - 1(-1cos(3\u03c0((-2x - 1)/(-1x + 3))) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "94", "dataset": "MATH"}