{"messages": [{"content": "How many zeros does the function f(x) = -2(-2sin(1\u03c0(3((-2x + 2)/(-3x + 2))^2 - 4((-2x + 2)/(-3x + 2)) + 4) - 3) - 2)^2 + 3(-2sin(1\u03c0(3((-2x + 2)/(-3x + 2))^2 - 4((-2x + 2)/(-3x + 2)) + 4) - 3) - 2) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((2(-1(-3x)^2 + 5(-3x) - 1) + 2)/(2(-1(-3x)^2 + 5(-3x) - 1) - 3)) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0(-3(3|((-2x)/(2x - 1))| - 3)^2 + 1(3|((-2x)/(2x - 1))| - 3) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "172", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-3sin(3\u03c0(2|(4x^2 + 3x - 5) + 1| - 3)) + 1) + 1)/(-2(-3sin(3\u03c0(2|(4x^2 + 3x - 5) + 1| - 3)) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "908", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-1((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3))^2 + 5((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3)) - 1)^2 + 2(-1((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3))^2 + 5((3(-3|x - 2|) - 1)/(-3(-3|x - 2|) - 3)) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(1(4(3x^2 - 5x)^2 + 3(3x^2 - 5x) - 3) - 3) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "966", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(1|((3(5x^2 - 4x) + 1)/(3(5x^2 - 4x))) - 2| - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(5(3cos(3\u03c0((2x)/(-3x + 1)) + 2) + 2) - 2))/(-3(5(3cos(3\u03c0((2x)/(-3x + 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": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-2(2|((1x + 3)/(3x - 2)) - 2| + 1) + 1) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(3cos(2\u03c0(-4(-5x^2 + 3x - 2)^2 + 2(-5x^2 + 3x - 2) - 3) + 2) + 1) + 1)/(-1(3cos(2\u03c0(-4(-5x^2 + 3x - 2)^2 + 2(-5x^2 + 3x - 2) - 3) + 2) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "563", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1((-1(4(1cos(3\u03c0x + 2) + 1) - 2) - 1)/(2(4(1cos(3\u03c0x + 2) + 1) - 2) - 3)) + 2)/(2((-1(4(1cos(3\u03c0x + 2) + 1) - 2) - 1)/(2(4(1cos(3\u03c0x + 2) + 1) - 2) - 3)) + 3) equals zero.\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 (3(1(2cos(1\u03c0(1x^2 + 4x + 4) - 3) + 2) - 3))/(-2(1(2cos(1\u03c0(1x^2 + 4x + 4) - 3) + 2) - 3) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "208", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-2((-1(1x^2 - 1x - 1) - 2)/(-3(1x^2 - 1x - 1) + 2))) - 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-3(-1(-3sin(1\u03c0x - 1) - 2) - 1) + 2)/(1(-1(-3sin(1\u03c0x - 1) - 2) - 1) - 2))^2 - 5((-3(-1(-3sin(1\u03c0x - 1) - 2) - 1) + 2)/(1(-1(-3sin(1\u03c0x - 1) - 2) - 1) - 2)) - 5 = 0 have in the range [-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|(-2e^(-2(2(4x^2 - 1x + 2)^2 + 2(4x^2 - 1x + 2))) - 1)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-4(4(-2|x + 2| + 3) - 1) - 2) - 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-2cos(2\u03c0(4(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) - 1) + 2) - 1))/(-1(-2cos(2\u03c0(4(-2|x - 3| - 1)^2 + 4(-2|x - 3| - 1) - 1) + 2) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1493", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-2sin(1\u03c0(3(4x^2 - 2x - 4)^2 - 2(4x^2 - 2x - 4) + 4) - 1) + 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "551", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1cos(3\u03c0((-1(-1x^2 - 4x - 3) + 1)/(2(-1x^2 - 4x - 3) + 1)) - 1)) + 1)/(-1(1cos(3\u03c0((-1(-1x^2 - 4x - 3) + 1)/(2(-1x^2 - 4x - 3) + 1)) - 1))) equals zero.\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) = 2|(-2|(4(-3cos(1\u03c0x + 3) - 2) + 5) + 2| + 2) + 3| - 3 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 (1(1|(-3(2|x| - 2) + 1) - 2| - 2) + 1)/(3(1|(-3(2|x| - 2) + 1) - 2| - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-3|(-1|(1x^2 + 5x + 5) - 1| + 2) + 1| + 1) + 3)/(-2(-3|(-1|(1x^2 + 5x + 5) - 1| + 2) + 1| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-2(-2sin(1\u03c0(3|x - 2|) - 3) - 1) - 3) + 4 equals zero.\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) = -2((-3(-3cos(2\u03c0((-3x - 2)/(2x - 3)) + 1) + 1) + 2)/(1(-3cos(2\u03c0((-3x - 2)/(2x - 3)) + 1) + 1) + 1))^2 - 3((-3(-3cos(2\u03c0((-3x - 2)/(2x - 3)) + 1) + 1) + 2)/(1(-3cos(2\u03c0((-3x - 2)/(2x - 3)) + 1) + 1) + 1)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(2(-3(4x + 1)^2 + 2(4x + 1))^2 - 5(-3(4x + 1)^2 + 2(4x + 1)))^2 + 1(2(-3(4x + 1)^2 + 2(4x + 1))^2 - 5(-3(4x + 1)^2 + 2(4x + 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(4(3(4x^2 + 3x - 4)^2 + 5(4x^2 + 3x - 4) - 3) + 4) + 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(2|(4(2|x + 2| + 3)^2 + 1(2|x + 2| + 3) + 4) + 3|) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1212", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-1(-2(3x + 2)^2 - 2(3x + 2) + 4)^2 - 5(-2(3x + 2)^2 - 2(3x + 2) + 4) - 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(1((-3(3x - 5) - 3)/(-2(3x - 5) + 3))^2 + 3((-3(3x - 5) - 3)/(-2(3x - 5) + 3)) + 2) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3e^(2(-3(4(-3x^2 + 3x + 5) + 1)^2 + 5(4(-3x^2 + 3x + 5) + 1) - 2)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(1cos(3\u03c0(-1|(-1x^2 - 2x + 2)| - 1) - 1) - 1)^2 + 4(1cos(3\u03c0(-1|(-1x^2 - 2x + 2)| - 1) - 1) - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "606", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(2(-4(-3|x + 1| + 2))^2 + 5(-4(-3|x + 1| + 2)) - 1))/(-2(2(-4(-3|x + 1| + 2))^2 + 5(-4(-3|x + 1| + 2)) - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1e^(2(-1((3(-3x^2 - 5x + 1))/(-2(-3x^2 - 5x + 1) + 3))^2 - 5((3(-3x^2 - 5x + 1))/(-2(-3x^2 - 5x + 1) + 3)) - 5)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((1(2sin(2\u03c0(-2|x - 1| + 3) + 3)) - 1)/(-3(2sin(2\u03c0(-2|x - 1| + 3) + 3)))) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0((1((1(3x^2 - 4) - 3)/(-3(3x^2 - 4) + 4)) + 1)/(-2((1(3x^2 - 4) - 3)/(-3(3x^2 - 4) + 4)) + 1)) - 2) - 1 equals zero.\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) = -3sin(1\u03c0((-2((-3(-2|x + 2| + 2))/(-1(-2|x + 2| + 2) + 2)) + 3)/(3((-3(-2|x + 2| + 2))/(-1(-2|x + 2| + 2) + 2)) + 3)) + 1) - 1 where -10 \u2264 x \u2264 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) = (-1(1(-2|(-3sin(2\u03c0x - 2) + 1) - 1| + 3)^2 + 5(-2|(-3sin(2\u03c0x - 2) + 1) - 1| + 3) + 3))/(3(1(-2|(-3sin(2\u03c0x - 2) + 1) - 1| + 3)^2 + 5(-2|(-3sin(2\u03c0x - 2) + 1) - 1| + 3) + 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 1((1(3(-3sin(1\u03c0x - 3) - 1) - 4) + 1)/(3(3(-3sin(1\u03c0x - 3) - 1) - 4) - 1)) - 5 = 0 have in the range [-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) = -4(-1(3(3cos(3\u03c0x + 1) + 2) - 3) + 2)^2 - 1(-1(3(3cos(3\u03c0x + 1) + 2) - 3) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2|(-3(1x + 5) - 3) - 2|)^2 - 5(2|(-3(1x + 5) - 3) - 2|) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(4(2|(4x^2 + 4)| - 2) - 3) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1194", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-4(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2))^2 + 3(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2)) + 1))/(3(-4(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2))^2 + 3(5(-1x^2 - 4x + 2)^2 + 5(-1x^2 - 4x + 2)) + 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(4(5(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) + 1)^2 + 5(5(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) + 1) + 2) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1058", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0(4(3(3x^2 - 2x - 3)^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": "480", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(1|((-2((-2x - 3)/(1x)) - 2)/(3((-2x - 3)/(1x)) - 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": "25", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(1(2|((1(5x^2 + 1x - 4) + 1)/(-3(5x^2 + 1x - 4))) + 2| - 2)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(1(-3(-5x^2 - 5x - 2) - 2)^2 + 5) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "431", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0((-2(-1(-3x - 4) - 5) - 2)/(1(-1(-3x - 4) - 5)))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3|((-1(-1|x - 1| + 1))/(-1(-1|x - 1| + 1) - 2)) + 1| + 1)^2 - 5(-3|((-1(-1|x - 1| + 1))/(-1(-1|x - 1| + 1) - 2)) + 1| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-1(4(3sin(3\u03c0x + 2) - 1) - 5) + 4) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(-2|(-5(-2|x - 1| - 2) + 3) + 1| + 1) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "199", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-4(-4(1|x - 2| - 2)^2 + 3(1|x - 2| - 2))^2 + 5)^2 + 4(-4(-4(1|x - 2| - 2)^2 + 3(1|x - 2| - 2))^2 + 5) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(2|(5(1x^2 + 5x + 2)^2 - 3) - 1| + 2) - 3| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(-3((-1(-5x) - 3)/(-3(-5x) - 1)) + 1) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(-2((-2(-3|x - 3|) - 2)/(-2(-3|x - 3|) + 3)) - 3) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2|((-2((2x)/(1x + 1)) - 2)/(-1((2x)/(1x + 1)))) - 1| + 1)^2 + 1(-2|((-2((2x)/(1x + 1)) - 2)/(-1((2x)/(1x + 1)))) - 1| + 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(3(1|(-3|x + 1| + 2)| - 2) + 4) - 2)/(-2(3(1|(-3|x + 1| + 2)| - 2) + 4) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((2(1(-2cos(2\u03c0x + 1) + 1)^2 - 3(-2cos(2\u03c0x + 1) + 1) - 1) + 3)/(2(1(-2cos(2\u03c0x + 1) + 1)^2 - 3(-2cos(2\u03c0x + 1) + 1) - 1) - 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2|(4(1x^2 - 5x + 4)^2 - 2(1x^2 - 5x + 4)) - 2| - 2) + 1)/(2(2|(4(1x^2 - 5x + 4)^2 - 2(1x^2 - 5x + 4)) - 2| - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 2)/(2(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 1))^2 - 4((3(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 2)/(2(-3(-1|x + 3|)^2 - 1(-1|x + 3|) + 3) - 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0((3(-3((-1x - 2)/(3x + 3)) + 4) - 2)/(-2(-3((-1x - 2)/(3x + 3)) + 4) - 2)) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-4(1sin(3\u03c0(-4x + 1) - 1) - 2) - 5) - 1)/(1(-4(1sin(3\u03c0(-4x + 1) - 1) - 2) - 5)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(5(2cos(1\u03c0(1|x + 1|) - 2) + 2)^2 + 5(2cos(1\u03c0(1|x + 1|) - 2) + 2) - 5) + 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": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(-1(-1|(3x^2 + 3x - 4) + 2| + 2) + 1) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "744", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(4((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3))^2 + 5((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3)) - 3) + 1)/(-2(4((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3))^2 + 5((2(1|x - 1| - 3) - 2)/(3(1|x - 1| - 3) + 3)) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0((-2(-1|(-5x - 3) + 2| + 1) + 2)/(2(-1|(-5x - 3) + 2| + 1) + 2)) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1e^(2(3|(3(1|x - 1| - 3) + 3) + 3| - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1(3cos(2\u03c0(-3x^2 - 4x - 1) - 1) + 2) + 1) - 2)/(1(1(3cos(2\u03c0(-3x^2 - 4x - 1) - 1) + 2) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "528", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(2(4x - 5)^2 - 4(4x - 5) - 1))/(2(2(4x - 5)^2 - 4(4x - 5) - 1) + 3)) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((-2(2cos(1\u03c0((1x - 1)/(-2x + 3))) + 2) - 2)/(2(2cos(1\u03c0((1x - 1)/(-2x + 3))) + 2) - 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(4(-2(-1x^2 - 5x + 5) + 1)^2 - 4(-2(-1x^2 - 5x + 5) + 1)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(3\u03c0(1(1|(2x^2 - 3x + 5) - 1| + 2) - 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "541", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2((2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) + 2)/(2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) - 3)) - 2)/(-2((2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) + 2)/(2(-2(3|x + 3| - 2)^2 + 5(3|x + 3| - 2) - 1) - 3)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3(-1(3x^2 - 4x - 4) + 4)^2 - 4(-1(3x^2 - 4x - 4) + 4) + 5) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-1|(4(-1|x - 1| + 3)^2 + 5(-1|x - 1| + 3) - 1) - 2| + 2) + 3)/(-1(-1|(4(-1|x - 1| + 3)^2 + 5(-1|x - 1| + 3) - 1) - 2| + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-2|(1sin(3\u03c0(2|x| + 1) + 1)) + 1| - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(1|(-5(-1cos(1\u03c0x + 2) + 2) + 3) + 3| - 1) - 2)/(-1(1|(-5(-1cos(1\u03c0x + 2) + 2) + 3) + 3| - 1) - 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": "Find the number of x-intercepts of the function f(x) = 4(-5(-3sin(2\u03c0(-3x^2 - 1x + 4) + 3) - 2) - 5) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1115", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0(-2|(2(-2|x - 1| + 2) + 3) - 1| - 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "157", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|((2(3(3|x - 1| - 1) - 5) - 3)/(3(3(3|x - 1| - 1) - 5) - 1)) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-2((1(2cos(3\u03c0x - 2) + 1) + 2)/(1(2cos(3\u03c0x - 2) + 1) - 2))^2 - 4((1(2cos(3\u03c0x - 2) + 1) + 2)/(1(2cos(3\u03c0x - 2) + 1) - 2)) - 1))/(-1(-2((1(2cos(3\u03c0x - 2) + 1) + 2)/(1(2cos(3\u03c0x - 2) + 1) - 2))^2 - 4((1(2cos(3\u03c0x - 2) + 1) + 2)/(1(2cos(3\u03c0x - 2) + 1) - 2)) - 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": "How many zeros does the function f(x) = -1((1((-3(-2sin(3\u03c0x + 3) - 3) + 2)/(-3(-2sin(3\u03c0x + 3) - 3) - 2)) - 2)/(3((-3(-2sin(3\u03c0x + 3) - 3) + 2)/(-3(-2sin(3\u03c0x + 3) - 3) - 2)) + 3))^2 - 5((1((-3(-2sin(3\u03c0x + 3) - 3) + 2)/(-3(-2sin(3\u03c0x + 3) - 3) - 2)) - 2)/(3((-3(-2sin(3\u03c0x + 3) - 3) + 2)/(-3(-2sin(3\u03c0x + 3) - 3) - 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": "Find the number of x-intercepts of the function f(x) = 3((1(3(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 2) + 1)/(3(3(-1|x + 2| + 2)^2 - 2(-1|x + 2| + 2) - 2) - 1)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-2|((-3(-2sin(2\u03c0x + 1) + 2) - 1)/(-2(-2sin(2\u03c0x + 1) + 2) - 2)) - 1|) - 2| - 3 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) = 3(-3|(1(-2x^2 - 3x)^2 + 5(-2x^2 - 3x) - 3) - 2|) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(3(-2cos(2\u03c0(5x + 4) - 3) + 1) - 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(1sin(2\u03c0((-3(-3|x + 2| + 3) + 2)/(1(-3|x + 2| + 3) + 3)) - 1) - 3) + 3| 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(3((-1(-1|x + 1| + 3) + 1)/(1(-1|x + 1| + 3) - 2))^2 - 4((-1(-1|x + 1| + 3) + 1)/(1(-1|x + 1| + 3) - 2)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(4((2(3x^2 - 2x - 3) + 2)/(-3(3x^2 - 2x - 3) + 2)) + 2) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-2|(2|(2sin(2\u03c0x + 2))| + 1) - 2| - 2) - 2)/(1(-2|(2|(2sin(2\u03c0x + 2))| + 1) - 2| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(-1cos(2\u03c0((2(-1|x + 1|) - 3)/(2(-1|x + 1|))) + 2) + 2) - 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(4(-2|((2x - 2)/(-2x - 3)) + 3| + 2) - 2)^2 + 1(4(-2|((2x - 2)/(-2x - 3)) + 3| + 2) - 2) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-2e^(-1(5(2|x + 2|) - 5)) + 2) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0((3(-4(4x^2 - 4x - 4)^2 + 2(4x^2 - 4x - 4) + 4) + 1)/(-2(-4(4x^2 - 4x - 4)^2 + 2(4x^2 - 4x - 4) + 4) - 3))) - 1 equals zero.\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 -5((-1(-2cos(3\u03c0(-2|x + 3| + 3) + 3)) - 2)/(2(-2cos(3\u03c0(-2|x + 3| + 3) + 3)) - 3))^2 + 5((-1(-2cos(3\u03c0(-2|x + 3| + 3) + 3)) - 2)/(2(-2cos(3\u03c0(-2|x + 3| + 3) + 3)) - 3)) = 0 have in the range [-10, 10]?\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) = (-1(3cos(1\u03c0(2|((3x)/(-1x - 3))| + 2) - 2) - 1) + 1)/(-2(3cos(1\u03c0(2|((3x)/(-1x - 3))| + 2) - 2) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-1((-2(2|x + 1| - 1) - 1)/(-1(2|x + 1| - 1) + 2)) - 4)^2 + 1(-1((-2(2|x + 1| - 1) - 1)/(-1(2|x + 1| - 1) + 2)) - 4) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-1(5(3x^2 + 3x)^2 - 1(3x^2 + 3x) + 2)^2 + 4(5(3x^2 + 3x)^2 - 1(3x^2 + 3x) + 2) + 5) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-2|(1(3sin(2\u03c0x - 1) - 2) + 1) - 3| + 1) + 3| - 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": "Find the number of x-intercepts of the function f(x) = -2|(2|(-4(-4x^2 + 4x + 1)^2 - 5(-4x^2 + 4x + 1) + 1) + 1|) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(2((-1(-3sin(2\u03c0x + 3) + 1))/(1(-3sin(2\u03c0x + 3) + 1) + 2))^2 - 2((-1(-3sin(2\u03c0x + 3) + 1))/(1(-3sin(2\u03c0x + 3) + 1) + 2)) - 5) - 3 = 0 have in the range [-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|(-2cos(1\u03c0((-2x - 1)/(-1x - 1)) - 1) - 1) + 3| - 1) + 1)/(2(1|(-2cos(1\u03c0((-2x - 1)/(-1x - 1)) - 1) - 1) + 3| - 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-1|(2|(3sin(2\u03c0x + 3) + 3) - 3| - 1) - 2| + 2) - 1)/(-3(-1|(2|(3sin(2\u03c0x + 3) + 3) - 3| - 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": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-2(-3(-1sin(2\u03c0x) - 1) - 4)^2 - 3(-3(-1sin(2\u03c0x) - 1) - 4) + 3)^2 - 2(-2(-3(-1sin(2\u03c0x) - 1) - 4)^2 - 3(-3(-1sin(2\u03c0x) - 1) - 4) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-2|((1(3|x + 2| - 3) - 1)/(2(3|x + 2| - 3) - 1)) - 3|) + 1)/(3(-2|((1(3|x + 2| - 3) - 1)/(2(3|x + 2| - 3) - 1)) - 3|) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(3|(3(5x^2 + 2x - 2)^2 + 1(5x^2 + 2x - 2) - 1)| - 2)^2 + 2(3|(3(5x^2 + 2x - 2)^2 + 1(5x^2 + 2x - 2) - 1)| - 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(4(-1(4x + 5) - 1) + 4) + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(4(2cos(3\u03c0(1|x - 2|) + 2) + 1)^2 + 2(2cos(3\u03c0(1|x - 2|) + 2) + 1) + 2) - 3| - 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) = -4(1|(-3sin(1\u03c0((2x + 3)/(1x - 2)) + 1) + 2) - 2| - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "133", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-2(-1cos(1\u03c0(-1|x + 3| - 1) + 1))^2 + 4) - 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": "How many zeros does the function f(x) = 2(-3|(3sin(3\u03c0(4x^2 - 5x + 3) - 2)) + 2| + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1517", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(2\u03c0(1|(2|(2x + 2) + 1| + 1)| - 3) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(-4((1(1x - 4) - 1)/(-1(1x - 4) + 2)) + 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(2(-1sin(1\u03c0(5x - 2) - 1) + 3) - 3) - 3)/(-3(2(-1sin(1\u03c0(5x - 2) - 1) + 3) - 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = (-3(-1(2|(1x + 3) + 2| - 3)^2 + 2) - 2)/(2(-1(2|(1x + 3) + 2| - 3)^2 + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3|(1|(3|x - 1| - 1) + 3| - 3) - 1| - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1(-3(1x + 5)^2 - 5(1x + 5) + 4)^2 - 5(-3(1x + 5)^2 - 5(1x + 5) + 4) - 5) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0(1(-3(1x - 4)^2 + 3(1x - 4) - 1)^2 - 2(-3(1x - 4)^2 + 3(1x - 4) - 1) + 4) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1204", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(1\u03c0(-1(4(-2x - 4) + 5)^2 - 2(4(-2x - 4) + 5) - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1582", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-1|(-2|(4x^2 - 2x + 4) - 2| + 1) + 1|) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "658", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(1|(-1(1sin(3\u03c0x + 3) - 1) + 4) - 3| - 2) + 2 = 0 have in the range [-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) = 2cos(2\u03c0(-2(-2(-5x^2 + 5x - 2)^2 + 2(-5x^2 + 5x - 2) + 4)^2 - 2(-2(-5x^2 + 5x - 2)^2 + 2(-5x^2 + 5x - 2) + 4) + 2) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-3cos(1\u03c0(-5(-5x^2 - 4x) + 3) - 1)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "904", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(2|(-2sin(2\u03c0((-1x - 2)/(-1x)) + 3) - 1) + 2| + 1) - 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(2|(2|(5x^2 + 3x) + 2| - 1) + 1| + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1605", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1\u03c0(-4((-2((3x)/(-1x - 3)) + 1)/(2((3x)/(-1x - 3)) + 2))^2 + 1((-2((3x)/(-1x - 3)) + 1)/(2((3x)/(-1x - 3)) + 2)) - 2) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "261", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((2(-4(-5x - 1)^2 - 3(-5x - 1)) + 2)/(2(-4(-5x - 1)^2 - 3(-5x - 1))))^2 - 4((2(-4(-5x - 1)^2 - 3(-5x - 1)) + 2)/(2(-4(-5x - 1)^2 - 3(-5x - 1)))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-2sin(1\u03c0(2|(-1|x - 3| - 2) - 2| - 3) + 3) + 3)^2 - 3(-2sin(1\u03c0(2|(-1|x - 3| - 2) - 2| - 3) + 3) + 3) - 3 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(-4(4(-3sin(3\u03c0x + 1) + 3)^2 - 3(-3sin(3\u03c0x + 1) + 3) - 1) + 4) + 2)/(2(-4(4(-3sin(3\u03c0x + 1) + 3)^2 - 3(-3sin(3\u03c0x + 1) + 3) - 1) + 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-1((-3(3cos(1\u03c0x + 1) - 3) - 2)/(-1(3cos(1\u03c0x + 1) - 3))) - 2) + 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 solutions does the equation -5(5(-5(-2sin(2\u03c0x - 1) + 2)^2 + 3(-2sin(2\u03c0x - 1) + 2) + 1) - 1)^2 - 2(5(-5(-2sin(2\u03c0x - 1) + 2)^2 + 3(-2sin(2\u03c0x - 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": "15", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(1|(4(5x - 2) + 1) + 1| - 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-2sin(3\u03c0(4(-4x - 3)^2 + 3(-4x - 3) - 2) - 3))| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "890", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-3sin(2\u03c0(2((3x + 2)/(1x + 3))^2 - 3((3x + 2)/(1x + 3)) + 2) + 2) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "337", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-2sin(3\u03c0(-4(-4x - 4)^2 + 4) - 3) + 1) + 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1589", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1sin(2\u03c0(2((2x + 1)/(-1x + 2))) + 1) + 1) - 2)/(2(1sin(2\u03c0(2((2x + 1)/(-1x + 2))) + 1) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(-1(1(5x^2 - 3x - 3) + 4) - 5) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1085", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(1|(2sin(2\u03c0(-2|x + 2| + 3) - 2)) + 1| - 1) + 1)/(3(1|(2sin(2\u03c0(-2|x + 2| + 3) - 2)) + 1| - 1) - 1) 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 zeros does the function f(x) = 1(1cos(3\u03c0(-3(2|x - 3| + 2)^2 + 1) + 2) + 3)^2 - 3(1cos(3\u03c0(-3(2|x - 3| + 2)^2 + 1) + 2) + 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1122", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(1(-3sin(3\u03c0(5x - 2) + 3) - 1)^2 + 4(-3sin(3\u03c0(5x - 2) + 3) - 1) - 5)^2 + 2(1(-3sin(3\u03c0(5x - 2) + 3) - 1)^2 + 4(-3sin(3\u03c0(5x - 2) + 3) - 1) - 5) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "450", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-4(-4((-1x)/(2x + 2)) + 1)^2 + 2(-4((-1x)/(2x + 2)) + 1) + 1)^2 + 3(-4(-4((-1x)/(2x + 2)) + 1)^2 + 2(-4((-1x)/(2x + 2)) + 1) + 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((-2(3|(-2cos(3\u03c0x + 2) + 3) - 3|))/(-2(3|(-2cos(3\u03c0x + 2) + 3) - 3|) + 3))| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-2(2((2x + 2)/(3x - 2))^2 - 3((2x + 2)/(3x - 2)) - 4) - 3)/(-1(2((2x + 2)/(3x - 2))^2 - 3((2x + 2)/(3x - 2)) - 4) - 1))^2 + 4((-2(2((2x + 2)/(3x - 2))^2 - 3((2x + 2)/(3x - 2)) - 4) - 3)/(-1(2((2x + 2)/(3x - 2))^2 - 3((2x + 2)/(3x - 2)) - 4) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1(-3|(-3|x + 2| + 3) - 3| + 2)^2 - 1(-3|(-3|x + 2| + 3) - 3| + 2) - 1)^2 - 3(1(-3|(-3|x + 2| + 3) - 3| + 2)^2 - 1(-3|(-3|x + 2| + 3) - 3| + 2) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4((3(2|(-1sin(3\u03c0x) - 1) - 1|) - 3)/(1(2|(-1sin(3\u03c0x) - 1) - 1|) + 3))^2 - 2((3(2|(-1sin(3\u03c0x) - 1) - 1|) - 3)/(1(2|(-1sin(3\u03c0x) - 1) - 1|) + 3)) - 4 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 zeros does the function f(x) = 1(5(1|(-3cos(2\u03c0x + 3) - 2) + 1| - 1)^2 - 1(1|(-3cos(2\u03c0x + 3) - 2) + 1| - 1) - 1)^2 + 5(5(1|(-3cos(2\u03c0x + 3) - 2) + 1| - 1)^2 - 1(1|(-3cos(2\u03c0x + 3) - 2) + 1| - 1) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(1|((3((-2x + 3)/(-1x + 3)) + 1)/(3((-2x + 3)/(-1x + 3)) + 2)) + 1| - 1)^2 + 4(1|((3((-2x + 3)/(-1x + 3)) + 1)/(3((-2x + 3)/(-1x + 3)) + 2)) + 1| - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2sin(1\u03c0((2(1x - 1) - 2)/(-2(1x - 1) + 1)) - 1) + 3) + 3)/(1(-2sin(1\u03c0((2(1x - 1) - 2)/(-2(1x - 1) + 1)) - 1) + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(1cos(2\u03c0(4((-3x - 1)/(-2x + 3)) + 3) + 3) - 1))/(2(1cos(2\u03c0(4((-3x - 1)/(-2x + 3)) + 3) + 3) - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-3(3|(3sin(3\u03c0x + 1) - 2)| - 2) - 1)/(-1(3|(3sin(3\u03c0x + 1) - 2)| - 2) + 2)) - 3| + 1 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 zeros does the function f(x) = 1cos(2\u03c0(2(-3(-2x^2 - 5x + 2)^2 - 1(-2x^2 - 5x + 2) - 5) + 5) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1304", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2(-5(-4x^2 - 3x + 5)^2 + 4(-4x^2 - 3x + 5)) + 4)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-1|(2(-1x - 5)^2 - 5(-1x - 5) - 2) - 3| + 1) - 3)/(1(-1|(2(-1x - 5)^2 - 5(-1x - 5) - 2) - 3| + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(1sin(2\u03c0(-1|(2x^2 + 2x - 1) - 2| - 3) - 1) + 2)^2 + 1(1sin(2\u03c0(-1|(2x^2 + 2x - 1) - 2| - 3) - 1) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-2((1(-1cos(1\u03c0x - 2) - 1) + 3)/(3(-1cos(1\u03c0x - 2) - 1) + 1))^2 + 3) - 2)/(2(-2((1(-1cos(1\u03c0x - 2) - 1) + 3)/(3(-1cos(1\u03c0x - 2) - 1) + 1))^2 + 3) - 1) = 0 have in the range [-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) = 2sin(2\u03c0(-2((3((2x - 1)/(3x - 2)) + 3)/(2((2x - 1)/(3x - 2)) + 3))^2 - 4((3((2x - 1)/(3x - 2)) + 3)/(2((2x - 1)/(3x - 2)) + 3)) - 3) + 3) have in the interval [-10, 10]?\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) = 2sin(3\u03c0(-1|(4(-1|x - 3|)^2 + 3(-1|x - 3|) - 4) + 2| + 2) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1364", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3sin(2\u03c0(-1((-1x - 3)/(1x + 1)) - 2) + 3) - 1) have in the interval [-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) = 1cos(3\u03c0(4(1|(3|x - 1| + 1) + 1|) - 5) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "346", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-2(-1|(3x - 2) - 2| + 1)^2 - 4(-1|(3x - 2) - 2| + 1)) + 3)/(3(-2(-1|(3x - 2) - 2| + 1)^2 - 4(-1|(3x - 2) - 2| + 1)) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4((-1(5(3sin(3\u03c0x) - 3) + 1) - 2)/(-3(5(3sin(3\u03c0x) - 3) + 1) - 1)) = 0 have in the range [-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|((-1(-2(2x^2 - 4)^2 + 2(2x^2 - 4) + 1) - 3)/(-1(-2(2x^2 - 4)^2 + 2(2x^2 - 4) + 1) + 2)) + 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(2cos(1\u03c0((3(3x - 2))/(2(3x - 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": "18", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(1|(-4((2x + 3)/(-2x + 3))^2 - 3) + 1| - 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "309", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-3sin(2\u03c0(-2|(3x + 4) - 2| - 2) + 2) - 1))/(2(-3sin(2\u03c0(-2|(3x + 4) - 2| - 2) + 2) - 1) + 1) 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": "Determine the number of values x in [-10, 10] where f(x) = -2(1((2((-1x + 3)/(-2x - 1)))/(2((-1x + 3)/(-2x - 1)) + 1))^2 - 1((2((-1x + 3)/(-2x - 1)))/(2((-1x + 3)/(-2x - 1)) + 1)) - 4)^2 - 4(1((2((-1x + 3)/(-2x - 1)))/(2((-1x + 3)/(-2x - 1)) + 1))^2 - 1((2((-1x + 3)/(-2x - 1)))/(2((-1x + 3)/(-2x - 1)) + 1)) - 4) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2((-1(-3|(3|x - 3|) - 1| + 3) - 1)/(2(-3|(3|x - 3|) - 1| + 3) - 1)) + 3)/(2((-1(-3|(3|x - 3|) - 1| + 3) - 1)/(2(-3|(3|x - 3|) - 1| + 3) - 1))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-4((-1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3))^2 + 3((-1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3)) + 1) - 3)/(2(-4((-1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3))^2 + 3((-1(-2|x - 3| + 2) + 3)/(-3(-2|x - 3| + 2) - 3)) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-2(1|(2x - 2) + 3|) + 2)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2((2(-1sin(3\u03c0(3|x - 1| + 2) + 1) - 1) - 2)/(-1(-1sin(3\u03c0(3|x - 1| + 2) + 1) - 1) + 2)) + 3)/(-2((2(-1sin(3\u03c0(3|x - 1| + 2) + 1) - 1) - 2)/(-1(-1sin(3\u03c0(3|x - 1| + 2) + 1) - 1) + 2)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-1((-1(5x - 5) - 3)/(3(5x - 5) + 1))^2 - 2((-1(5x - 5) - 3)/(3(5x - 5) + 1)) + 5)^2 - 5(-1((-1(5x - 5) - 3)/(3(5x - 5) + 1))^2 - 2((-1(5x - 5) - 3)/(3(5x - 5) + 1)) + 5) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1(1(-3x + 4)^2 - 2(-3x + 4) - 2)^2 - 2(1(-3x + 4)^2 - 2(-3x + 4) - 2) - 3) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(2cos(1\u03c0(1(-2x - 2) - 4) - 2) + 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": "How many solutions does the equation 1(2(2(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) + 1)^2 - 2(2(2|x - 2| - 2)^2 + 5(2|x - 2| - 2) + 1) - 4) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(-1(1(5x - 3)^2 - 3(5x - 3) - 1)^2 + 1(1(5x - 3)^2 - 3(5x - 3) - 1) + 5)| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-5(2(-2sin(3\u03c0x + 3) + 1) + 1)^2 + 2(2(-2sin(3\u03c0x + 3) + 1) + 1) - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(-3(3(-2x^2 - 3x - 4) - 4) - 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1423", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((-2(-1|(2|x - 3| - 3) - 1|) + 3)/(1(-1|(2|x - 3| - 3) - 1|) + 2)) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(4((-2(5x^2 + 2x - 5) + 1)/(1(5x^2 + 2x - 5) - 2))^2 + 4) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((3(3|(2x^2 + 2x - 1)| - 2) - 2)/(1(3|(2x^2 + 2x - 1)| - 2) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(1(3cos(3\u03c0(-1|x - 3|) + 3) - 3) + 3) + 5 equals zero.\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 1|(-2(3|(2sin(3\u03c0x + 3)) - 2| - 1) - 1) + 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((-1(3|(1x + 1) + 3| - 1) - 1)/(3(3|(1x + 1) + 3| - 1) - 2))^2 + 5((-1(3|(1x + 1) + 3| - 1) - 1)/(3(3|(1x + 1) + 3| - 1) - 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2sin(1\u03c0(-3|(1x - 4)|) + 3) + 1)^2 - 5(2sin(1\u03c0(-3|(1x - 4)|) + 3) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-3sin(1\u03c0((-3(2|x + 3| + 2) + 2)/(1(2|x + 3| + 2) + 1)) - 2) - 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-3sin(3\u03c0(-2|(5x^2 - 5x - 2)| - 1))) + 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "847", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0(4(-3|(-3x + 1) - 2| + 2) + 5)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-4(-1(1x^2 + 5x - 1) - 5) + 2)^2 + 4(-4(-1(1x^2 + 5x - 1) - 5) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1((1(5x^2 - 5x - 2) - 2)/(-3(5x^2 - 5x - 2) + 2)) - 1)^2 - 5(-1((1(5x^2 - 5x - 2) - 2)/(-3(5x^2 - 5x - 2) + 2)) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((3(5((1x - 1)/(1x + 2))^2 + 3((1x - 1)/(1x + 2)) - 1) + 1)/(1(5((1x - 1)/(1x + 2))^2 + 3((1x - 1)/(1x + 2)) - 1) - 2))^2 + 4((3(5((1x - 1)/(1x + 2))^2 + 3((1x - 1)/(1x + 2)) - 1) + 1)/(1(5((1x - 1)/(1x + 2))^2 + 3((1x - 1)/(1x + 2)) - 1) - 2)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2|(-1sin(2\u03c0((2x - 1)/(1x)) - 3) + 3) - 3| + 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(3\u03c0(1(2(-5x + 4) + 2) + 3) - 2) 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": "Find the number of x-intercepts of the function f(x) = -1(-1((-1(1x^2 + 1x) - 2)/(-1(1x^2 + 1x) + 2)) - 3)^2 + 3(-1((-1(1x^2 + 1x) - 2)/(-1(1x^2 + 1x) + 2)) - 3) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(4((1(-3x^2 + 3x + 5) - 1)/(3(-3x^2 + 3x + 5) - 2))^2 - 5((1(-3x^2 + 3x + 5) - 1)/(3(-3x^2 + 3x + 5) - 2))) - 3)/(3(4((1(-3x^2 + 3x + 5) - 1)/(3(-3x^2 + 3x + 5) - 2))^2 - 5((1(-3x^2 + 3x + 5) - 1)/(3(-3x^2 + 3x + 5) - 2))) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1|(-1(2cos(2\u03c0x - 2) + 3)^2 - 4(2cos(2\u03c0x - 2) + 3) - 1) + 2| + 2)| - 3 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) = (-1(-3(-4(-2sin(3\u03c0x - 2) - 1) + 5) + 4) + 1)/(-2(-3(-4(-2sin(3\u03c0x - 2) - 1) + 5) + 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(3|(4(2x + 5) - 4) - 1| - 3) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1440", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(-5(-4(1x^2 - 5x - 3)^2 + 5(1x^2 - 5x - 3) - 2) + 1) - 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1106", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(3\u03c0((1(4((-3x + 2)/(3x)) + 5) + 2)/(1(4((-3x + 2)/(3x)) + 5)))) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(3|(1(-2|x + 3|) + 3) + 2|) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-2(1cos(3\u03c0(3x + 5)) - 3) - 2)/(-1(1cos(3\u03c0(3x + 5)) - 3) + 2)) + 2)/(2((-2(1cos(3\u03c0(3x + 5)) - 3) - 2)/(-1(1cos(3\u03c0(3x + 5)) - 3) + 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1(-1(-2|x + 1| + 3)^2 - 2(-2|x + 1| + 3) + 3)^2 + 3(-1(-2|x + 1| + 3)^2 - 2(-2|x + 1| + 3) + 3) - 5) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(5(5((-1x - 3)/(-1x + 2)) + 2)^2 - 4(5((-1x - 3)/(-1x + 2)) + 2))^2 - 5(5(5((-1x - 3)/(-1x + 2)) + 2)^2 - 4(5((-1x - 3)/(-1x + 2)) + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-1cos(3\u03c0(-1((2x - 3)/(2x + 2))^2 + 1((2x - 3)/(2x + 2))) + 3) + 3) - 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0((3(4((-2x - 1)/(-3x - 2))^2 - 2((-2x - 1)/(-3x - 2)) - 4) - 3)/(-3(4((-2x - 1)/(-3x - 2))^2 - 2((-2x - 1)/(-3x - 2)) - 4) + 2)) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(3(-3sin(2\u03c0(-2|x + 3| + 2) - 1) + 2) - 2) + 2)/(-1(3(-3sin(2\u03c0(-2|x + 3| + 2) - 1) + 2) - 2)) = 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": "Determine the number of values x in [-10, 10] where f(x) = (-2(3cos(3\u03c0(-3(2x + 1) - 1) - 1) - 2))/(1(3cos(3\u03c0(-3(2x + 1) - 1) - 1) - 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(4(-4((2x - 3)/(-1x - 3))^2 + 2) - 1)^2 - 2(4(-4((2x - 3)/(-1x - 3))^2 + 2) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(4(-3(1cos(2\u03c0x + 2) - 2)^2 + 5) - 2)^2 + 4(4(-3(1cos(2\u03c0x + 2) - 2)^2 + 5) - 2) - 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": "Find the number of x-intercepts of the function f(x) = 2(-1(-1|(-3x^2 + 2x + 5) - 1|) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|((-3((-1(-1x^2 + 5x - 1) + 1)/(3(-1x^2 + 5x - 1) + 1)) + 1)/(-3((-1(-1x^2 + 5x - 1) + 1)/(3(-1x^2 + 5x - 1) + 1)) + 2)) - 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(2(-1(4x^2 - 5x - 5)^2 - 5(4x^2 - 5x - 5) - 1)^2 + 1(-1(4x^2 - 5x - 5)^2 - 5(4x^2 - 5x - 5) - 1) + 4) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "268", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-1cos(1\u03c0(-5(-2|x + 1| + 3) - 4) - 1)) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(5(-3|((2x)/(2x + 3)) + 2| + 2) + 2) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-3(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5)^2 + 4(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5) + 5) - 3)/(1(-3(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5)^2 + 4(-4(-2|x - 1|)^2 - 5(-2|x - 1|) + 5) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(2|(4(-2x^2 + 5)^2 + 2(-2x^2 + 5) - 2)| + 3) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1244", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(2sin(2\u03c0((3((-3x - 1)/(-3x + 1)) - 3)/(-3((-3x - 1)/(-3x + 1)) + 1)) + 1) + 1) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1(-1cos(2\u03c0(-2|x - 1| + 1) + 3) - 3) + 4))/(-3(1(-1cos(2\u03c0(-2|x - 1| + 1) + 3) - 3) + 4) + 1) 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": "How many solutions does the equation 5(5((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1))^2 - 4((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1)) - 1)^2 - 1(5((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1))^2 - 4((-1((1x - 3)/(2x)) + 1)/(1((1x - 3)/(2x)) + 1)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(3\u03c0((-2(-1(-1|x - 1| + 2)^2 - 1(-1|x - 1| + 2) + 1) - 2)/(-2(-1(-1|x - 1| + 2)^2 - 1(-1|x - 1| + 2) + 1) + 1)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-4(-2cos(3\u03c0(-2|x + 3| + 3) + 2) - 3) - 4) - 3| + 3 where -10 \u2264 x \u2264 10.\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) = -5((-2(-2cos(1\u03c0(-2|x - 1| - 2) - 1) + 3) + 3)/(-1(-2cos(1\u03c0(-2|x - 1| - 2) - 1) + 3) + 2))^2 + 3((-2(-2cos(1\u03c0(-2|x - 1| - 2) - 1) + 3) + 3)/(-1(-2cos(1\u03c0(-2|x - 1| - 2) - 1) + 3) + 2)) + 3 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": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3\u03c0(5(2(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1) + 2)^2 + 1(2(-2|x + 3| - 1)^2 + 3(-2|x + 3| - 1) + 2) + 3)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "530", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(3((-3(3x^2 - 3x - 5) - 2)/(2(3x^2 - 3x - 5) + 2))^2 - 1((-3(3x^2 - 3x - 5) - 2)/(2(3x^2 - 3x - 5) + 2)) - 5) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(1|(-3(-1|x| + 3)^2 + 1(-1|x| + 3) + 3) + 1| - 2) - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "169", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-5(5(2x - 4)^2 - 3(2x - 4) - 5)^2 + 2(5(2x - 4)^2 - 3(2x - 4) - 5) - 3) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "341", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2((2(-3cos(2\u03c0x + 3) - 1) - 2)/(2(-3cos(2\u03c0x + 3) - 1)))) - 1)/(-1(2((2(-3cos(2\u03c0x + 3) - 1) - 2)/(2(-3cos(2\u03c0x + 3) - 1)))) + 2) equals zero.\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) = 1sin(3\u03c0((-3((-2(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1))) + 2)/(2((-2(2|x + 1| + 1) + 2)/(2(2|x + 1| + 1))) + 2)) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(3(-3|(1x^2 - 5)| + 3)^2 - 2(-3|(1x^2 - 5)| + 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(1sin(3\u03c0(-4(-3|x| - 3) - 1)) - 3) + 3)/(2(1sin(3\u03c0(-4(-3|x| - 3) - 1)) - 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "718", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((-2((1(3cos(1\u03c0x + 3) - 2) - 2)/(1(3cos(1\u03c0x + 3) - 2) + 2)) - 3)/(2((1(3cos(1\u03c0x + 3) - 2) - 2)/(1(3cos(1\u03c0x + 3) - 2) + 2))))^2 + 5 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 solutions does the equation 3sin(3\u03c0(1|((2(2|x - 1| + 1) + 3)/(-1(2|x - 1| + 1) - 3)) - 3| - 3) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(4(-2|(1x - 4) - 1| - 2)^2 - 4(-2|(1x - 4) - 1| - 2) - 2) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1173", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-1(-2|(3|x + 3| - 1) - 2| - 1)^2 - 5(-2|(3|x + 3| - 1) - 2| - 1) - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(-2(4(-2|x + 1| - 2) + 3)^2 - 4(4(-2|x + 1| - 2) + 3)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1453", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(2sin(3\u03c0(-1|(-2x + 3) + 1| - 2) - 1) - 1) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(-3(2(1|x + 1| - 3) - 2)^2 - 4(2(1|x + 1| - 3) - 2) - 1) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "937", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2sin(3\u03c0(4((-3x + 3)/(-1x + 3)) + 3) + 3) - 2))/(2(2sin(3\u03c0(4((-3x + 3)/(-1x + 3)) + 3) + 3) - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-5(-2(-3cos(1\u03c0x + 1) + 1)^2 + 4(-3cos(1\u03c0x + 1) + 1) - 1)^2 + 1(-2(-3cos(1\u03c0x + 1) + 1)^2 + 4(-3cos(1\u03c0x + 1) + 1) - 1))^2 + 3(-5(-2(-3cos(1\u03c0x + 1) + 1)^2 + 4(-3cos(1\u03c0x + 1) + 1) - 1)^2 + 1(-2(-3cos(1\u03c0x + 1) + 1)^2 + 4(-3cos(1\u03c0x + 1) + 1) - 1)) - 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 zeros does the function f(x) = 3cos(1\u03c0(-2(-3|(-1x - 3)|) - 3) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1(-2|(1e^(-2x) - 2) - 3| + 3)^2 + 3(-2|(1e^(-2x) - 2) - 3| + 3) + 4)^2 + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-4(3sin(3\u03c0(-1|x - 2| + 2)) - 2) - 1) + 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((-3((3(-2cos(2\u03c0x + 3) - 1) - 1)/(3(-2cos(2\u03c0x + 3) - 1) + 3)) - 2)/(-1((3(-2cos(2\u03c0x + 3) - 1) - 1)/(3(-2cos(2\u03c0x + 3) - 1) + 3)) + 2)) = 0 have in the range [-10, 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) = 2(-1cos(2\u03c0(-2(4x^2 + 3x - 5) + 1) + 2) + 2)^2 - 1(-1cos(2\u03c0(-2(4x^2 + 3x - 5) + 1) + 2) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1130", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(1cos(1\u03c0(-1(-2x^2 - 1x)^2 + 1(-2x^2 - 1x) + 3)) + 1)| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1302", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-2(3(3|x - 2| + 1) - 3) - 2)/(-2(3(3|x - 2| + 1) - 3) + 3)) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(2|(4(-3x^2 + 3x) + 1) - 1| - 2) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(1(1|(1x^2 + 4x - 5)| - 2)^2 + 5(1|(1x^2 + 4x - 5)| - 2) - 4) - 3)/(2(1(1|(1x^2 + 4x - 5)| - 2)^2 + 5(1|(1x^2 + 4x - 5)| - 2) - 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1|((-2(3sin(1\u03c0x - 1) + 3) + 3)/(-1(3sin(1\u03c0x - 1) + 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0((-2((-2(-4x + 5) - 1)/(1(-4x + 5))) + 1)/(1((-2(-4x + 5) - 1)/(1(-4x + 5))))) + 3) + 2 equals zero.\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) = -2(-5(-3|(1x + 5)|)^2 + 1(-3|(1x + 5)|) + 2)^2 + 1(-5(-3|(1x + 5)|)^2 + 1(-3|(1x + 5)|) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1(3cos(3\u03c0(1|x - 1| + 1) - 1) - 2) + 4) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(1(5((1x + 2)/(2x - 1)) + 3) + 4) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-5(1|(-3x^2 + 3) + 2|)^2 + 5(1|(-3x^2 + 3) + 2|) + 3) + 2)/(1(-5(1|(-3x^2 + 3) + 2|)^2 + 5(1|(-3x^2 + 3) + 2|) + 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(3|(3|(3x - 3) - 2| - 1) + 1| - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(2|((-1((1x + 1)/(-3x - 1)) - 1)/(-3((1x + 1)/(-3x - 1)) + 2)) + 1| - 2) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(4(4(-2|x|)^2 + 3(-2|x|) - 4)^2 + 3(4(-2|x|)^2 + 3(-2|x|) - 4) + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-2|(-3(4x - 1) + 3) + 1| + 1)^2 - 4(-2|(-3(4x - 1) + 3) + 1| + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1(2((2x - 2)/(-1x))^2 + 5((2x - 2)/(-1x)) + 2) + 5)^2 - 3(-1(2((2x - 2)/(-1x))^2 + 5((2x - 2)/(-1x)) + 2) + 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(2cos(2\u03c0((-2(1|x - 1| + 1) + 2)/(-1(1|x - 1| + 1) - 3)) + 3) - 1) + 3)/(1(2cos(2\u03c0((-2(1|x - 1| + 1) + 2)/(-1(1|x - 1| + 1) - 3)) + 3) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-2cos(3\u03c0((-2(4x - 3) - 2)/(-3(4x - 3) - 1)) + 1)) - 1| have in the interval [-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|(1|(-3sin(3\u03c0(1x + 5) + 3) + 3) + 1| - 3) + 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) = 2sin(2\u03c0(-5((-3(-4x^2 - 3x - 3) - 3)/(1(-4x^2 - 3x - 3) + 2))^2 + 2((-3(-4x^2 - 3x - 3) - 3)/(1(-4x^2 - 3x - 3) + 2)) - 3) + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "179", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1sin(1\u03c0(1(4x - 2) + 1) + 1) - 3) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(2sin(3\u03c0(3((-3x - 1)/(-3x + 4))^2 + 5((-3x - 1)/(-3x + 4)) + 1) - 2) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "148", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(1|((-2(-5x^2 - 4x - 2) - 2)/(-1(-5x^2 - 4x - 2) - 2)) - 1| - 1) - 1)/(1(1|((-2(-5x^2 - 4x - 2) - 2)/(-1(-5x^2 - 4x - 2) - 2)) - 1| - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(1(4(1x + 2)^2 + 5(1x + 2) + 2)^2 - 1(4(1x + 2)^2 + 5(1x + 2) + 2) + 4)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "958", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((2(-2|(1x^2 + 2x - 4) + 3|) - 2)/(-1(-2|(1x^2 + 2x - 4) + 3|) - 3)) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1|(2|(-1x + 1) + 3| - 1) - 2| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(3|(1x^2 + 5x - 4) - 3| - 2) + 1) - 3)/(-1(-2(3|(1x^2 + 5x - 4) - 3| - 2) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(2(-5(-1x^2 + 4x + 1) - 1)^2 + 3(-5(-1x^2 + 4x + 1) - 1) - 1)^2 - 4(2(-5(-1x^2 + 4x + 1) - 1)^2 + 3(-5(-1x^2 + 4x + 1) - 1) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(2sin(3\u03c0((3(-4x + 4) + 2)/(-2(-4x + 4) - 1)) + 2) + 3) + 3)/(3(2sin(3\u03c0((3(-4x + 4) + 2)/(-2(-4x + 4) - 1)) + 2) + 3) - 2) equals zero.\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) = (-3(3(-5(-3sin(2\u03c0x - 2) - 2)^2 - 1(-3sin(2\u03c0x - 2) - 2)) + 3))/(-1(3(-5(-3sin(2\u03c0x - 2) - 2)^2 - 1(-3sin(2\u03c0x - 2) - 2)) + 3) + 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 zeros does the function f(x) = 1|((-3((3(1|x + 1| - 1) + 2)/(-3(1|x + 1| - 1) - 3)) + 1)/(-2((3(1|x + 1| - 1) + 2)/(-3(1|x + 1| - 1) - 3)) + 3)) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(4(-3(-2x^2 + 1x + 5)^2 - 4(-2x^2 + 1x + 5) + 3)^2 - 1(-3(-2x^2 + 1x + 5)^2 - 4(-2x^2 + 1x + 5) + 3)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3\u03c0((-2(4((3x - 2)/(-1x + 2)) - 1) - 3)/(-1(4((3x - 2)/(-1x + 2)) - 1))) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(3(-1(4x^2 + 2x - 1) - 2)^2 + 4(-1(4x^2 + 2x - 1) - 2) - 5) + 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(5(3((3x + 1)/(3x - 1)) + 3)^2 + 1(3((3x + 1)/(3x - 1)) + 3) - 5) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "374", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-3cos(1\u03c0((-1(1|x + 1| - 1) + 3)/(3(1|x + 1| - 1) - 1)) + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(1|(-2sin(2\u03c0((-3x)/(1x + 3)) + 2) + 1) - 3| - 2)^2 + 4(1|(-2sin(2\u03c0((-3x)/(1x + 3)) + 2) + 1) - 3| - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(1\u03c0((1(1(3x - 4) + 2) + 1)/(-3(1(3x - 4) + 2) + 4)) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3\u03c0(-2|(4(-2x + 5) - 4) - 1|) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "464", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(1|(-3((-2x)/(-1x - 2)) - 3)| - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "220", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0((-3(-2|((-3x + 1)/(-2x + 3)) - 3| + 2) - 1)/(-2(-2|((-3x + 1)/(-2x + 3)) - 3| + 2))) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(4(3|(-1x^2 - 3x) - 1| + 2)^2 + 1(3|(-1x^2 - 3x) - 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": "1464", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(1|(4(1x^2 - 3x - 2)^2 - 3(1x^2 - 3x - 2) - 5) + 3| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0(-1|(3|(-2|x| - 1) - 3| + 1) - 3| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0((1(5(-3x^2 + 5) + 5) - 1)/(1(5(-3x^2 + 5) + 5) - 3)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-2|(1(1|x - 1| - 3)^2 + 5(1|x - 1| - 3) - 5) - 2| + 3) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-1(-2cos(3\u03c0(2|x + 2| + 2) + 3) - 1)^2 + 4(-2cos(3\u03c0(2|x + 2| + 2) + 3) - 1)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-4(1(4x - 4) - 4)^2 + 3(1(4x - 4) - 4) + 1)^2 + 3(-4(1(4x - 4) - 4)^2 + 3(1(4x - 4) - 4) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2((-3(3|((1x - 2)/(-2x + 3))| - 2) - 3)/(-2(3|((1x - 2)/(-2x + 3))| - 2) + 1))^2 + 4((-3(3|((1x - 2)/(-2x + 3))| - 2) - 3)/(-2(3|((1x - 2)/(-2x + 3))| - 2) + 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2((-3(-2sin(3\u03c0(2|x + 3| + 2) + 2) + 2) - 2)/(-3(-2sin(3\u03c0(2|x + 3| + 2) + 2) + 2) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-1(4(3cos(3\u03c0x) + 2) + 5)^2 + 2(4(3cos(3\u03c0x) + 2) + 5)))/(1(-1(4(3cos(3\u03c0x) + 2) + 5)^2 + 2(4(3cos(3\u03c0x) + 2) + 5)) + 2) = 0 have in the range [-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) = 3|(3((2(1cos(2\u03c0x + 3) - 1) + 2)/(1(1cos(2\u03c0x + 3) - 1) + 3)) + 1) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2(3cos(3\u03c0(2|x + 1| - 1) + 2) + 2) - 5))/(-2(2(3cos(3\u03c0(2|x + 1| - 1) + 2) + 2) - 5) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1(-1e^(2(-2x^2 + 2x + 2)))^2 + 5(-1e^(2(-2x^2 + 2x + 2)))) - 2)/(-2(1(-1e^(2(-2x^2 + 2x + 2)))^2 + 5(-1e^(2(-2x^2 + 2x + 2)))) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1e^(-2(-1|(-4(-3x^2 + 2x + 3) - 5) + 1| + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(3(3(-3|x + 1| + 2) - 2) + 5)^2 + 5(3(3(-3|x + 1| + 2) - 2) + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(4((-2(4x^2 - 1x - 1) - 1)/(1(4x^2 - 1x - 1) + 2))^2 - 3((-2(4x^2 - 1x - 1) - 1)/(1(4x^2 - 1x - 1) + 2)) + 5) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(-2((3(-1|x| + 2))/(-1(-1|x| + 2) - 3)) - 5) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0(5(-3|(-1|x - 2| - 3) - 1| + 3) + 2) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-2(-5(-2cos(2\u03c0x + 3) - 1)^2 - 5(-2cos(2\u03c0x + 3) - 1) + 1) - 1)/(-1(-5(-2cos(2\u03c0x + 3) - 1)^2 - 5(-2cos(2\u03c0x + 3) - 1) + 1) + 2)))/(-2((-2(-5(-2cos(2\u03c0x + 3) - 1)^2 - 5(-2cos(2\u03c0x + 3) - 1) + 1) - 1)/(-1(-5(-2cos(2\u03c0x + 3) - 1)^2 - 5(-2cos(2\u03c0x + 3) - 1) + 1) + 2)) - 3) equals zero.\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 (-1(3cos(2\u03c0(3(1x^2 + 3x + 4) + 4) + 1)) - 1)/(2(3cos(2\u03c0(3(1x^2 + 3x + 4) + 4) + 1)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "732", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((-1(4(3sin(2\u03c0x + 1) + 2)^2 + 1(3sin(2\u03c0x + 1) + 2) - 2) + 1)/(-1(4(3sin(2\u03c0x + 1) + 2)^2 + 1(3sin(2\u03c0x + 1) + 2) - 2) + 2))^2 + 2((-1(4(3sin(2\u03c0x + 1) + 2)^2 + 1(3sin(2\u03c0x + 1) + 2) - 2) + 1)/(-1(4(3sin(2\u03c0x + 1) + 2)^2 + 1(3sin(2\u03c0x + 1) + 2) - 2) + 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-2(-2|(1x^2 + 4x - 4) + 2| - 3) - 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "832", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3((-1(-2|x + 1| + 2) - 2)/(-3(-2|x + 1| + 2) - 3)) - 2)^2 + 3(-3((-1(-2|x + 1| + 2) - 2)/(-3(-2|x + 1| + 2) - 3)) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((3((-2(-2cos(2\u03c0x + 3)) + 3)/(-2(-2cos(2\u03c0x + 3)) - 2)) + 1)/(-2((-2(-2cos(2\u03c0x + 3)) + 3)/(-2(-2cos(2\u03c0x + 3)) - 2)) + 3)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3|(-3sin(3\u03c0(1|x + 1| + 2) + 1) + 3) - 3| + 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1(3sin(3\u03c0((-2x + 1)/(1x + 2)) + 2) - 3) + 2)^2 + 1(1(3sin(3\u03c0((-2x + 1)/(1x + 2)) + 2) - 3) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0((3(4(-1x + 3)^2 - 5(-1x + 3) - 5) + 1)/(-2(4(-1x + 3)^2 - 5(-1x + 3) - 5) - 1)) - 1) + 1 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": "How many solutions does the equation -1((1(3sin(3\u03c0(1x^2 - 1x + 5) + 1) - 2) + 1)/(2(3sin(3\u03c0(1x^2 - 1x + 5) + 1) - 2))) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "93", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|((-2(4((1x - 1)/(-2x - 2))^2 + 5((1x - 1)/(-2x - 2)) - 1) + 2)/(3(4((1x - 1)/(-2x - 2))^2 + 5((1x - 1)/(-2x - 2)) - 1) - 1)) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(-4(-4(2x^2 + 4) + 2)^2 - 5(-4(2x^2 + 4) + 2)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0((3(-2(4x + 2)^2 - 1(4x + 2) - 1) + 1)/(-2(-2(4x + 2)^2 - 1(4x + 2) - 1) - 3))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(2|((2((-2x + 3)/(3x - 2)) - 2)/(-2((-2x + 3)/(3x - 2)) + 3)) - 1| + 1) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3|(-2(1sin(3\u03c0x - 2) - 1)^2 + 2(1sin(3\u03c0x - 2) - 1) + 3) + 3| + 1)^2 - 4(-3|(-2(1sin(3\u03c0x - 2) - 1)^2 + 2(1sin(3\u03c0x - 2) - 1) + 3) + 3| + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(-2|(-1((2x + 1)/(3x + 2))^2 - 4((2x + 1)/(3x + 2)) + 4) + 2| - 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-2cos(2\u03c0(4(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) - 5)) + 1) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(2\u03c0(-1|(-5((-1x - 3)/(-2x + 3))^2 - 5((-1x - 3)/(-2x + 3)) + 4) - 3| + 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "269", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-2|(1(2x - 3)^2 + 4(2x - 3) - 5) - 2| - 2) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0(-1((1(-1x^2 - 3x + 1))/(3(-1x^2 - 3x + 1) + 2))^2 + 4((1(-1x^2 - 3x + 1))/(3(-1x^2 - 3x + 1) + 2)) + 3) + 1) equals zero.\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) = 1sin(1\u03c0(4(1((-2x + 3)/(-1x + 2))^2 + 2((-2x + 3)/(-1x + 2)) - 2) - 4) - 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(-1|(3|(-5x + 4) - 3| - 3) - 3| - 2)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "414", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((2((-3(-3sin(2\u03c0x - 3) - 2) + 2)/(-1(-3sin(2\u03c0x - 3) - 2) + 2)) - 1)/(-3((-3(-3sin(2\u03c0x - 3) - 2) + 2)/(-1(-3sin(2\u03c0x - 3) - 2) + 2))))^2 + 1((2((-3(-3sin(2\u03c0x - 3) - 2) + 2)/(-1(-3sin(2\u03c0x - 3) - 2) + 2)) - 1)/(-3((-3(-3sin(2\u03c0x - 3) - 2) + 2)/(-1(-3sin(2\u03c0x - 3) - 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 2cos(3\u03c0(-5(-2|(2x + 5)|) + 3) + 3) = 0 have in the range [-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) = -3|(-5(3sin(3\u03c0((2x + 2)/(-1x - 3)) - 2) - 2)^2 - 4(3sin(3\u03c0((2x + 2)/(-1x - 3)) - 2) - 2) + 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0((3(-1(-5x - 2) + 2) - 3)/(-2(-1(-5x - 2) + 2) - 3))) + 2 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": "How many zeros does the function f(x) = 2|(4(-1|((2x + 3)/(-1x + 3)) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(2(1sin(2\u03c0(2|x - 2| + 2) + 3) - 1) + 3) - 5 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) = 2cos(1\u03c0(1(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) + 2)^2 - 1(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) + 2) - 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1285", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2|((3(-1x^2 - 3x + 1) + 2)/(-3(-1x^2 - 3x + 1) + 4)) - 3| + 1)^2 - 3(2|((3(-1x^2 - 3x + 1) + 2)/(-3(-1x^2 - 3x + 1) + 4)) - 3| + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(1\u03c0(-5(-1(2x)^2 - 2(2x) + 3) - 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1161", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-1sin(1\u03c0(-3|(-2x - 3) + 2| - 2) - 3) - 2)^2 - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3|(1cos(3\u03c0(-2x + 1) + 3) + 1) - 1| - 1) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-5(-3cos(2\u03c0(-3|x - 1| + 2) - 2) + 2) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2((-2(-2cos(1\u03c0(1x - 3) + 1) + 1) + 2)/(3(-2cos(1\u03c0(1x - 3) + 1) + 1) - 1)) + 3)/(2((-2(-2cos(1\u03c0(1x - 3) + 1) + 1) + 2)/(3(-2cos(1\u03c0(1x - 3) + 1) + 1) - 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 solutions does the equation -5(1|(-3(3|x - 1| - 3))| - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(2sin(3\u03c0(-1|(3x - 3) - 2| + 3)) - 2) + 1| where -10 \u2264 x \u2264 10.\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) = -2|((2(-3(2|x + 2|) + 2) + 1)/(-1(-3(2|x + 2|) + 2)))| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(4(1(1x - 3) + 3)^2 - 5(1(1x - 3) + 3) - 1)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1cos(2\u03c0((-2((2x + 2)/(-3x - 1)))/(1((2x + 2)/(-3x - 1)) + 1)) - 2))^2 + 1(-1cos(2\u03c0((-2((2x + 2)/(-3x - 1)))/(1((2x + 2)/(-3x - 1)) + 1)) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "182", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-2(-3(1x + 2)^2 + 5(1x + 2) + 1) + 1)^2 - 4(-2(-3(1x + 2)^2 + 5(1x + 2) + 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(2(1(-2|x - 2| - 2) + 1) + 4)^2 - 1(2(1(-2|x - 2| - 2) + 1) + 4) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3|(1cos(3\u03c0((-3x - 1)/(-1x + 3))))| + 1) - 3)/(1(-3|(1cos(3\u03c0((-3x - 1)/(-1x + 3))))| + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "239", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((-3(-3(3sin(3\u03c0x + 2) + 2)^2 + 5(3sin(3\u03c0x + 2) + 2) + 3) - 1)/(-3(-3(3sin(3\u03c0x + 2) + 2)^2 + 5(3sin(3\u03c0x + 2) + 2) + 3) - 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(3\u03c0(-5(-4((3x - 3)/(-2x + 1)) + 2)^2 + 5(-4((3x - 3)/(-2x + 1)) + 2) - 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "488", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2(-4(3sin(3\u03c0x + 1) - 2)^2 + 4) + 2)^2 + 3(2(-4(3sin(3\u03c0x + 1) - 2)^2 + 4) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1|((-2(1sin(2\u03c0x + 3) + 2) - 2)/(2(1sin(2\u03c0x + 3) + 2) - 3)) + 2| + 1)| - 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": "Determine the number of values x in [-10, 10] where f(x) = -5(3((1(3x + 4) - 2)/(2(3x + 4) + 3))^2 + 2((1(3x + 4) - 2)/(2(3x + 4) + 3)) - 3)^2 + 4(3((1(3x + 4) - 2)/(2(3x + 4) + 3))^2 + 2((1(3x + 4) - 2)/(2(3x + 4) + 3)) - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-2|(-1(1|x - 1| - 3) + 2)| + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-1|(1|(3x) + 3| - 1) - 1| + 2) + 2)/(2(-1|(1|(3x) + 3| - 1) - 1| + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0(-5((-1((2x - 2)/(1x)) + 3)/(2((2x - 2)/(1x)) + 2)) - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-3|(-3cos(3\u03c0(-3x^2 + 5x - 4) + 2)) + 1|) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "432", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(2sin(2\u03c0(2(2|x + 3|)^2 - 1(2|x + 3|)) - 1)) + 2)/(3(2sin(2\u03c0(2(2|x + 3|)^2 - 1(2|x + 3|)) - 1)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1068", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1sin(2\u03c0(-1((-2x + 3)/(1x + 1)) + 4) + 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1e^(-1(-1(2|(-3x^2 - 5x - 2) + 3| - 2)^2 - 5(2|(-3x^2 - 5x - 2) + 3| - 2) + 4)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3((-1(-4(3sin(2\u03c0x + 3) + 2) + 3) - 2)/(3(-4(3sin(2\u03c0x + 3) + 2) + 3) - 2)) + 2)/(-3((-1(-4(3sin(2\u03c0x + 3) + 2) + 3) - 2)/(3(-4(3sin(2\u03c0x + 3) + 2) + 3) - 2)) + 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": "Determine the number of values x in [-10, 10] where f(x) = -5(5(-4(-3x^2 + 5x - 1) - 5)^2 + 2(-4(-3x^2 + 5x - 1) - 5) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2e^(-1(-3|(-3|((1x - 1)/(-2x - 1)) + 3| + 2) + 2| + 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2((1(3cos(3\u03c0x) - 1) - 3)/(1(3cos(3\u03c0x) - 1)))^2 + 5((1(3cos(3\u03c0x) - 1) - 3)/(1(3cos(3\u03c0x) - 1))) + 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0((-2(4(-3|x + 2| + 2)^2 - 1(-3|x + 2| + 2) - 1) + 2)/(3(4(-3|x + 2| + 2)^2 - 1(-3|x + 2| + 2) - 1) + 3)) + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4)^2 + 1(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4) - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-3((1(3sin(3\u03c0x + 1) + 3) - 3)/(1(3sin(3\u03c0x + 1) + 3))) - 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 zeros does the function f(x) = (-2((1(-3sin(2\u03c0(-2|x - 2|) + 1) + 1) - 3)/(-2(-3sin(2\u03c0(-2|x - 2|) + 1) + 1) - 2)))/(2((1(-3sin(2\u03c0(-2|x - 2|) + 1) + 1) - 3)/(-2(-3sin(2\u03c0(-2|x - 2|) + 1) + 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": "Find the number of x-intercepts of the function f(x) = 4(-1|(-5(-5x^2 - 2x)^2 + 1(-5x^2 - 2x) + 2)| + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(-1((3(-4x - 2) + 3)/(-1(-4x - 2) + 3))^2 + 5((3(-4x - 2) + 3)/(-1(-4x - 2) + 3)) + 2) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "283", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-3(2|(2sin(1\u03c0x + 1) + 2) - 1|)^2 - 4(2|(2sin(1\u03c0x + 1) + 2) - 1|) + 3)| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3sin(2\u03c0((2(1x - 4) + 2)/(-2(1x - 4) + 3)) + 3) - 1) - 1)/(1(3sin(2\u03c0((2(1x - 4) + 2)/(-2(1x - 4) + 3)) + 3) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(3|(-1(3sin(2\u03c0x + 2) + 2)^2 + 5(3sin(2\u03c0x + 2) + 2)) + 2| - 2) + 2)/(-3(3|(-1(3sin(2\u03c0x + 2) + 2)^2 + 5(3sin(2\u03c0x + 2) + 2)) + 2| - 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": "Determine the number of values x in [-10, 10] where f(x) = (-3((2(-1(-3sin(1\u03c0x - 1) - 3)) + 1)/(1(-1(-3sin(1\u03c0x - 1) - 3)) - 2)) - 3)/(3((2(-1(-3sin(1\u03c0x - 1) - 3)) + 1)/(1(-1(-3sin(1\u03c0x - 1) - 3)) - 2))) equals zero.\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) = (3((2(-2sin(1\u03c0(-1x + 3) - 2) - 2) + 1)/(-1(-2sin(1\u03c0(-1x + 3) - 2) - 2) - 1)) + 3)/(1((2(-2sin(1\u03c0(-1x + 3) - 2) - 2) + 1)/(-1(-2sin(1\u03c0(-1x + 3) - 2) - 2) - 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1cos(1\u03c0(-1|(1|x + 1| + 3) - 3| - 2)) - 2) + 4 = 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": "How many zeros does the function f(x) = 4(-3cos(1\u03c0(-5(-2x^2 + 4x - 4)^2 - 4(-2x^2 + 4x - 4) + 1) - 1) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "841", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(3(-3(3|x + 1| + 2)^2 - 5(3|x + 1| + 2) - 3)^2 + 3(-3(3|x + 1| + 2)^2 - 5(3|x + 1| + 2) - 3) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "414", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-4(-2sin(2\u03c0((-3x)/(-3x + 2)) + 3) + 1)^2 - 2(-2sin(2\u03c0((-3x)/(-3x + 2)) + 3) + 1) + 3)^2 - 5(-4(-2sin(2\u03c0((-3x)/(-3x + 2)) + 3) + 1)^2 - 2(-2sin(2\u03c0((-3x)/(-3x + 2)) + 3) + 1) + 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-4(-2|(3|x| - 3) + 2| + 3)^2 + 4(-2|(3|x| - 3) + 2| + 3) + 5) + 3)/(3(-4(-2|(3|x| - 3) + 2| + 3)^2 + 4(-2|(3|x| - 3) + 2| + 3) + 5) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1)^2 - 3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1) + 2) + 2)/(-3(-3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1)^2 - 3(1(2|x| - 2)^2 + 3(2|x| - 2) - 1) + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-2|(3|((-2x + 2)/(-1x + 3)) + 3|) - 1| - 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "215", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(5(-1(-5x + 1)^2 - 4(-5x + 1) + 5)^2 + 2) - 3)/(1(5(-1(-5x + 1)^2 - 4(-5x + 1) + 5)^2 + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3sin(3\u03c0(1|((-2x + 3)/(-1x)) - 2| + 2) - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-4(-3(-3cos(1\u03c0x) - 1)^2 + 2(-3cos(1\u03c0x) - 1) + 1) - 2) + 5 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) = 2|(2cos(1\u03c0(-1|(3x^2 - 5x - 5) + 3|) - 1) - 3) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "586", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1e^(2((1(-1x^2 - 5x - 3))/(-1(-1x^2 - 5x - 3) + 2))) - 3)^2 - 3(1e^(2((1(-1x^2 - 5x - 3))/(-1(-1x^2 - 5x - 3) + 2))) - 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1)^2 + 3(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1) - 3) - 1)/(2(2(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1)^2 + 3(-1(3|x + 2| - 3)^2 - 4(3|x + 2| - 3) + 1) - 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(5(-1|(-1x + 1) - 1| + 2) + 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2((3(3|(3|x + 3| - 2) - 2| - 3))/(3(3|(3|x + 3| - 2) - 2| - 3) - 2)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(-2(-2|(5x^2 - 5) + 2| + 3) - 1) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1129", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-5(2cos(3\u03c0((3x - 2)/(-2x)) - 2) + 2) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5((-2(3(-3cos(3\u03c0x - 2) + 2)^2 + 4(-3cos(3\u03c0x - 2) + 2) + 1) + 2)/(-2(3(-3cos(3\u03c0x - 2) + 2)^2 + 4(-3cos(3\u03c0x - 2) + 2) + 1))) = 0 have in the range [-10, 10]?\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((-2(2|(2|x - 2|) - 1|) - 3)/(3(2|(2|x - 2|) - 1|) + 1))^2 - 5((-2(2|(2|x - 2|) - 1|) - 3)/(3(2|(2|x - 2|) - 1|) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(2(5(-3x^2 - 2x - 1) - 1) - 2) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "995", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2((3(1cos(2\u03c0((3x - 1)/(-1x + 2)) + 2)) - 1)/(2(1cos(2\u03c0((3x - 1)/(-1x + 2)) + 2)) + 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2|(1(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 3)| + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-2|(3e^(2((2x - 3)/(3x - 1))) - 3) - 1| + 2) + 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(-5(-1|(5x^2 - 5x + 2) + 2| + 1)^2 + 1(-1|(5x^2 - 5x + 2) + 2| + 1) + 5) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "644", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-5(-3sin(2\u03c0((3x - 3)/(2x + 1)) - 2) - 3)^2 + 2(-3sin(2\u03c0((3x - 3)/(2x + 1)) - 2) - 3) + 5)^2 - 5(-5(-3sin(2\u03c0((3x - 3)/(2x + 1)) - 2) - 3)^2 + 2(-3sin(2\u03c0((3x - 3)/(2x + 1)) - 2) - 3) + 5) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(2(2|(2|x + 1| - 3)| + 1)^2 - 2(2|(2|x + 1| - 3)| + 1))^2 - 1(2(2|(2|x + 1| - 3)| + 1)^2 - 2(2|(2|x + 1| - 3)| + 1)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(2(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5)^2 + 1(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5) - 3) + 1)/(1(2(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5)^2 + 1(-4((-3x + 1)/(-1x + 2))^2 + 3((-3x + 1)/(-1x + 2)) + 5) - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(2sin(2\u03c0((1((3x + 3)/(-2x + 1)) - 1)/(-3((3x + 3)/(-2x + 1)))) - 3) - 1) - 3)/(2(2sin(2\u03c0((1((3x + 3)/(-2x + 1)) - 1)/(-3((3x + 3)/(-2x + 1)))) - 3) - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-2(3e^(-1((2x + 3)/(-3x - 2))) - 1)^2 + 3(3e^(-1((2x + 3)/(-3x - 2))) - 1) + 3)^2 - 5(-2(3e^(-1((2x + 3)/(-3x - 2))) - 1)^2 + 3(3e^(-1((2x + 3)/(-3x - 2))) - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2(-2sin(1\u03c0(-1x^2 + 5x - 1) + 1) + 3)^2 + 5(-2sin(1\u03c0(-1x^2 + 5x - 1) + 1) + 3) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(-3|((2((2x + 1)/(2x - 3)) + 2)/(-3((2x + 1)/(2x - 3)) - 1))| - 2) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(1(-3|(5x) + 2| + 1) + 2)| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0((-1((2(-1|x| + 2))/(2(-1|x| + 2) - 1)) + 2)/(-3((2(-1|x| + 2))/(2(-1|x| + 2) - 1)) + 1)) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|((-1(5(-4x^2 - 2x + 3)^2 + 3(-4x^2 - 2x + 3) - 3) + 3)/(-2(5(-4x^2 - 2x + 3)^2 + 3(-4x^2 - 2x + 3) - 3) - 2)) - 3| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(-4((3(-4x^2 - 1x - 4) - 3)/(-2(-4x^2 - 1x - 4))) + 1) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1\u03c0(5((-3((1x - 2)/(-1x - 3)) - 1)/(-3((1x - 2)/(-1x - 3)))) - 3) - 3) + 1 equals zero.\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) = -3((-2(-1|(4x + 2) - 1| + 1) - 1)/(-2(-1|(4x + 2) - 1| + 1) + 3))^2 - 4((-2(-1|(4x + 2) - 1| + 1) - 1)/(-2(-1|(4x + 2) - 1| + 1) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3)^2 + 2(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3))^2 + 5(1(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3)^2 + 2(3cos(1\u03c0((-3x + 3)/(-2x + 3))) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(-2((-1(-2x^2 + 4x + 4) - 1)/(-1(-2x^2 + 4x + 4) - 3))^2 + 3((-1(-2x^2 + 4x + 4) - 1)/(-1(-2x^2 + 4x + 4) - 3)) - 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|((2(-3(-3cos(3\u03c0x - 2) - 1)^2 + 5(-3cos(3\u03c0x - 2) - 1) - 3) - 2)/(2(-3(-3cos(3\u03c0x - 2) - 1)^2 + 5(-3cos(3\u03c0x - 2) - 1) - 3) + 3)) + 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(3cos(2\u03c0(1|((1x - 1)/(-3x - 3)) + 3| + 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": "43", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-2(-3cos(2\u03c0(4x^2 + 4x - 1)) - 1) + 1)/(1(-3cos(2\u03c0(4x^2 + 4x - 1)) - 1) + 1))^2 - 2((-2(-3cos(2\u03c0(4x^2 + 4x - 1)) - 1) + 1)/(1(-3cos(2\u03c0(4x^2 + 4x - 1)) - 1) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1132", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-2|(-3(4x - 3)^2 + 4(4x - 3)) + 2| + 1) + 1)/(-1(-2|(-3(4x - 3)^2 + 4(4x - 3)) + 2| + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((3(-3sin(1\u03c0(4x - 4) + 2) - 2) - 1)/(1(-3sin(1\u03c0(4x - 4) + 2) - 2) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((3(-4(2x^2 + 2x + 1)^2 + 3(2x^2 + 2x + 1) + 5) + 2)/(2(-4(2x^2 + 2x + 1)^2 + 3(2x^2 + 2x + 1) + 5) + 2)) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0(3|(3(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1)| - 2) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1071", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1(-3cos(1\u03c0(-4x^2 - 1x + 1) - 2) - 3)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-4((-3((-3x + 3)/(-1x - 1)))/(-2((-3x + 3)/(-1x - 1)) + 3))^2 - 5((-3((-3x + 3)/(-1x - 1)))/(-2((-3x + 3)/(-1x - 1)) + 3)) + 4)| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-4((-1(-1sin(1\u03c0x - 3)) + 2)/(-3(-1sin(1\u03c0x - 3)) + 1))^2 - 5((-1(-1sin(1\u03c0x - 3)) + 2)/(-3(-1sin(1\u03c0x - 3)) + 1)) + 1)^2 + 1(-4((-1(-1sin(1\u03c0x - 3)) + 2)/(-3(-1sin(1\u03c0x - 3)) + 1))^2 - 5((-1(-1sin(1\u03c0x - 3)) + 2)/(-3(-1sin(1\u03c0x - 3)) + 1)) + 1) + 5 equals zero.\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) = 3sin(3\u03c0(-3(-4((-2x + 2)/(-1x - 2))^2 + 1((-2x + 2)/(-1x - 2)) + 3) + 1) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "644", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1(1(-2|x - 2| + 3)^2 + 4(-2|x - 2| + 3) + 4)^2 - 3(1(-2|x - 2| + 3)^2 + 4(-2|x - 2| + 3) + 4) - 5) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0((3(-1(3x^2 + 1x - 5) + 2) + 1)/(-1(-1(3x^2 + 1x - 5) + 2) + 2)) - 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-1(-2|(1x + 5) - 1| - 2)^2 - 3(-2|(1x + 5) - 1| - 2) + 3) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(5((3(-2cos(3\u03c0x + 2) + 1) - 1)/(-2(-2cos(3\u03c0x + 2) + 1) - 3))^2 + 3((3(-2cos(3\u03c0x + 2) + 1) - 1)/(-2(-2cos(3\u03c0x + 2) + 1) - 3)) - 5)^2 - 5(5((3(-2cos(3\u03c0x + 2) + 1) - 1)/(-2(-2cos(3\u03c0x + 2) + 1) - 3))^2 + 3((3(-2cos(3\u03c0x + 2) + 1) - 1)/(-2(-2cos(3\u03c0x + 2) + 1) - 3)) - 5) - 2 where -10 \u2264 x \u2264 10.\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) = (-3(-3sin(2\u03c0((3((-2x + 2)/(2x + 2)) + 2)/(-1((-2x + 2)/(2x + 2)))) - 3)) - 1)/(2(-3sin(2\u03c0((3((-2x + 2)/(2x + 2)) + 2)/(-1((-2x + 2)/(2x + 2)))) - 3)) + 2) 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": "How many zeros does the function f(x) = (1(-3|(3cos(1\u03c0(5x - 5)) + 2)|) + 3)/(2(-3|(3cos(1\u03c0(5x - 5)) + 2)|) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(1cos(1\u03c0(5((3x - 1)/(-2x)) - 1))) - 2 = 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": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(-3(3|x|) + 4) + 3|) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(2\u03c0(4(-3|(1x + 3) + 2| + 3) - 2) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1(2|(-2|x + 2|) - 1| - 2) + 3)^2 + 5(-1(2|(-2|x + 2|) - 1| - 2) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(-3|(-1(-2|x - 1|)^2 + 5) + 2| - 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1074", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-5(3|(3|x + 3| - 2) - 2|)^2 + 2(3|(3|x + 3| - 2) - 2|) + 3) - 1)/(-1(-5(3|(3|x + 3| - 2) - 2|)^2 + 2(3|(3|x + 3| - 2) - 2|) + 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|((-1(-1cos(3\u03c0((-2x - 2)/(2x - 3)) + 2) + 1) + 1)/(2(-1cos(3\u03c0((-2x - 2)/(2x - 3)) + 2) + 1) - 3)) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0(2(2(4x + 1) + 4) + 5) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "154", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(3|(2(-5x^2 + 2x)^2 - 1(-5x^2 + 2x) - 4) + 1| - 2) - 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3((1(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 3)/(2(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 2)) + 3)/(-2((1(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 3)/(2(1(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 2) + 2)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-5(5((-2x - 1)/(2x - 3)) - 5)^2 + 4(5((-2x - 1)/(2x - 3)) - 5) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1380", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-3(-3(-3x - 1)^2 + 1(-3x - 1) + 1) - 3) + 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((3(3sin(1\u03c0(-5x + 4) + 2) - 1) + 2)/(-3(3sin(1\u03c0(-5x + 4) + 2) - 1) - 3)) 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 zeros does the function f(x) = 1(-1|(-3(-3cos(3\u03c0x - 1) - 1)^2 + 2(-3cos(3\u03c0x - 1) - 1) + 3) - 3| + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|((1(-2(1|x + 2| - 1) + 5))/(1(-2(1|x + 2| - 1) + 5) - 3)) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-2|(5(-2x + 5)^2 - 2(-2x + 5) - 5) + 2|) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(3cos(3\u03c0(-5((-1x - 2)/(1x + 3)) + 2) - 3) + 1) + 3)/(-2(3cos(3\u03c0(-5((-1x - 2)/(1x + 3)) + 2) - 3) + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1(2sin(3\u03c0((-1x + 1)/(1x - 3)) + 1) + 2)^2 + 3(2sin(3\u03c0((-1x + 1)/(1x - 3)) + 1) + 2) + 5)^2 + 4(-1(2sin(3\u03c0((-1x + 1)/(1x - 3)) + 1) + 2)^2 + 3(2sin(3\u03c0((-1x + 1)/(1x - 3)) + 1) + 2) + 5) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(-1|(-1(3|x + 1| - 1)^2 + 5(3|x + 1| - 1) - 5) + 1| + 1) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1190", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(1((-2(-4x^2 + 4x + 4) + 2)/(-1(-4x^2 + 4x + 4) + 3))^2 + 5((-2(-4x^2 + 4x + 4) + 2)/(-1(-4x^2 + 4x + 4) + 3)) + 5) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(1((-1((3x)/(-1x - 1)) + 3)/(-2((3x)/(-1x - 1))))^2 + 4((-1((3x)/(-1x - 1)) + 3)/(-2((3x)/(-1x - 1)))) - 1)) + 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 zeros does the function f(x) = 2(-2cos(1\u03c0(-3|(5x^2 + 1x - 1) + 3| + 3) - 2))^2 - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1329", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(4(-3cos(1\u03c0(-3|x - 2| + 3) - 3) + 1) + 1)^2 - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-1sin(3\u03c0(-5((-3x)/(-1x - 3))^2 - 1((-3x)/(-1x - 3)) + 2))) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "706", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(1\u03c0(-3|(4((3x - 3)/(-3x - 1))^2 - 5((3x - 3)/(-3x - 1)) - 3) + 1| - 1) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "140", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-2|(2cos(1\u03c0(1x^2 - 4x + 4) - 3)) - 1| + 3) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-2(2|(-1|x + 1| + 1) + 3|)) + 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0(-2|(-3(1x + 4)^2) - 1| + 3) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1485", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(1(1|((3x - 3)/(1x + 2)) + 3|) - 4) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2|(-1|(3sin(1\u03c0x + 2) + 2)| + 1) + 1| + 2) + 1)/(-3(-2|(-1|(3sin(1\u03c0x + 2) + 2)| + 1) + 1| + 2)) equals zero.\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) = (2(3sin(1\u03c0((-1(3|x + 1| - 1) + 2)/(1(3|x + 1| - 1))) + 3) + 2))/(3(3sin(1\u03c0((-1(3|x + 1| - 1) + 2)/(1(3|x + 1| - 1))) + 3) + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(-3|(1(-2x - 5) - 1) - 1| + 2) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(3sin(2\u03c0(-1(3x^2 - 4x + 4) + 3) + 2) - 2))/(-2(3sin(2\u03c0(-1(3x^2 - 4x + 4) + 3) + 2) - 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "562", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1\u03c0(3(-2((2x)/(-3x + 4)) - 2) + 5) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2cos(1\u03c0(2|((2x + 2)/(-3x + 4)) - 3|) + 2) + 2)^2 + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-1(2cos(3\u03c0(-2|x + 2| - 2) + 1) - 1) - 5) + 2| = 0 have in the range [-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) = 1sin(2\u03c0(-1((-1(-4x + 2) - 3)/(-2(-4x + 2)))^2 - 1((-1(-4x + 2) - 3)/(-2(-4x + 2)))) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(5(2|(2|x - 1| - 3) + 2|) - 5) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "378", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(1(-2cos(1\u03c0((-2x - 2)/(2x - 1)) + 1))^2 + 5(-2cos(1\u03c0((-2x - 2)/(2x - 1)) + 1)) - 5)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-4((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2))^2 - 3((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2)) + 2)^2 + 3(-4((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2))^2 - 3((2(-2x^2 - 4x + 5) - 1)/(1(-2x^2 - 4x + 5) + 2)) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(5(2(4x^2 + 1x - 3))^2 - 4(2(4x^2 + 1x - 3)) + 4)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "571", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3((3(-2|(3sin(2\u03c0x) + 1)| + 2) + 2)/(-1(-2|(3sin(2\u03c0x) + 1)| + 2))) - 3)/(-1((3(-2|(3sin(2\u03c0x) + 1)| + 2) + 2)/(-1(-2|(3sin(2\u03c0x) + 1)| + 2)))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3sin(1\u03c0(-1(-3x^2 + 2x + 5)^2 - 2(-3x^2 + 2x + 5) - 2) + 3)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1093", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|((-1(-2sin(2\u03c0((1x + 3)/(-3x + 2)) + 1) + 1) - 1)/(1(-2sin(2\u03c0((1x + 3)/(-3x + 2)) + 1) + 1)))| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(3((2(2|x + 3| - 2) + 2)/(2(2|x + 3| - 2) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-2|(2sin(2\u03c0(-1x + 3)) - 3) + 2| + 1) + 2)/(1(-2|(2sin(2\u03c0(-1x + 3)) - 3) + 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": "Determine the number of values x in [-10, 10] where f(x) = (-2((2(-1(-3cos(3\u03c0x))) + 3)/(2(-1(-3cos(3\u03c0x))))) - 2)/(-3((2(-1(-3cos(3\u03c0x))) + 3)/(2(-1(-3cos(3\u03c0x))))) + 4) equals zero.\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) = 2|(-2(3(-1x - 1)^2 + 3(-1x - 1) + 3) + 4) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-3(3|(-2|x + 2| + 1) + 1| + 1) + 5)^2 - 1(-3(3|(-2|x + 2| + 1) + 1| + 1) + 5) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(3\u03c0(-2(3((3x - 3)/(-2x - 1)) - 3)^2 + 1(3((3x - 3)/(-2x - 1)) - 3) + 2) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "445", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(1cos(2\u03c0(-1(3x^2 - 5x - 5) - 2) - 1) + 1)^2 + 1(1cos(2\u03c0(-1(3x^2 - 5x - 5) - 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": "1033", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-1cos(3\u03c0(-1|(-5x - 2) - 3| + 2) + 2) - 1) - 1)/(3(-1cos(3\u03c0(-1|(-5x - 2) - 3| + 2) + 2) - 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1|(3(3sin(1\u03c0x - 2) - 1)^2 + 5(3sin(1\u03c0x - 2) - 1) - 1) + 1| - 2) + 2 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": "Find the number of x-intercepts of the function f(x) = -3((-3(-1(-5x^2 - 1x + 4)^2 + 3(-5x^2 - 1x + 4) - 1) + 2)/(3(-1(-5x^2 - 1x + 4)^2 + 3(-5x^2 - 1x + 4) - 1) - 1)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(1|(1|((3x + 2)/(2x + 3)) - 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": "52", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0(1|(3(1|x - 3| - 3) + 5) - 3| + 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(1(-2|(-3x + 5) + 1|)^2 + 2(-2|(-3x + 5) + 1|)) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1242", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1((1(-2cos(3\u03c0((2x + 3)/(1x - 3))) + 1))/(2(-2cos(3\u03c0((2x + 3)/(1x - 3))) + 1) + 2)) + 3)/(-2((1(-2cos(3\u03c0((2x + 3)/(1x - 3))) + 1))/(2(-2cos(3\u03c0((2x + 3)/(1x - 3))) + 1) + 2)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(-3(2|(1x - 5)| - 2) + 1) + 3) 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 1(3(-4(3sin(2\u03c0x - 3) + 1)) - 5)^2 + 5(3(-4(3sin(2\u03c0x - 3) + 1)) - 5) - 4 = 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": "Determine the number of values x in [-10, 10] where f(x) = 2(5(-2(1x^2 - 3x) + 5)^2 + 3(-2(1x^2 - 3x) + 5) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1|((-2(-3x^2 + 4x + 2) - 3)/(3(-3x^2 + 4x + 2))) - 3| + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(2|(-1(-1|x| - 3) - 1) + 2| - 2) + 2) + 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) = -1|(-3(1(3|x| + 1) - 5) - 4) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1((-3((-3(-1sin(3\u03c0x - 3)) - 1)/(-1(-1sin(3\u03c0x - 3)) + 2)) - 1)/(2((-3(-1sin(3\u03c0x - 3)) - 1)/(-1(-1sin(3\u03c0x - 3)) + 2)) + 2)) - 2)/(3((-3((-3(-1sin(3\u03c0x - 3)) - 1)/(-1(-1sin(3\u03c0x - 3)) + 2)) - 1)/(2((-3(-1sin(3\u03c0x - 3)) - 1)/(-1(-1sin(3\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) = 4(1(3e^(1(2x^2 + 3x - 1)) - 2)^2 - 1(3e^(1(2x^2 + 3x - 1)) - 2) - 2)^2 - 2(1(3e^(1(2x^2 + 3x - 1)) - 2)^2 - 1(3e^(1(2x^2 + 3x - 1)) - 2) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(-4(3((3x)/(-1x + 2)) - 4) + 1) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "393", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|(2(4x - 2)^2 + 4(4x - 2) - 2) + 2| + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1|(3(1x^2 + 2x + 1)^2 + 2(1x^2 + 2x + 1) + 2) - 1| - 2) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-1(1(-2|x - 1| - 3)^2 + 3(-2|x - 1| - 3) - 5) - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1708", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-2|(-1(1sin(3\u03c0x) - 2)^2 + 4) - 2| + 3) = 0 have in the range [-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) = 5(-1(2|(-1x^2 + 3)| + 1) + 4) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(1cos(3\u03c0(2|(3x - 1) - 3| + 2)) - 1)^2 + 5(1cos(3\u03c0(2|(3x - 1) - 3| + 2)) - 1) + 4 = 0 have in the range [-10, 10]?\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 3(1(-3sin(1\u03c0(-3x + 4)) + 1) - 1) - 5 = 0 have in the range [-10, 10]?\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) = 1|(-2(-2(1x^2 - 5x - 2)^2 - 3(1x^2 - 5x - 2) + 2) + 4)| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(2sin(3\u03c0(-2|(3|x - 2| - 3) - 1| + 1))) - 2)/(-3(2sin(3\u03c0(-2|(3|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": "360", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2|(1((1x + 2)/(3x - 2))^2 + 1((1x + 2)/(3x - 2)) - 3) - 2| + 1)^2 + 5(-2|(1((1x + 2)/(3x - 2))^2 + 1((1x + 2)/(3x - 2)) - 3) - 2| + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0(1((-2((3x + 2)/(-3x - 1)) - 3)/(-2((3x + 2)/(-3x - 1)) - 1))^2 + 3((-2((3x + 2)/(-3x - 1)) - 3)/(-2((3x + 2)/(-3x - 1)) - 1))) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(1|(3|(-1|x + 1| + 3) - 1| - 2) + 3| - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-3(2(1|x - 1| + 2) + 3) + 5) + 1) + 1 where -10 \u2264 x \u2264 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) = -1cos(1\u03c0(1((1(-3x + 1))/(-1(-3x + 1) - 2)) - 1) - 1) 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(2(2cos(3\u03c0(1|x - 1| - 3) + 1)) - 1)^2 + 4(2(2cos(3\u03c0(1|x - 1| - 3) + 1)) - 1) + 4 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 -2(-1|((2(-2x + 3) - 1)/(2(-2x + 3) + 1))| + 1)^2 - 5(-1|((2(-2x + 3) - 1)/(2(-2x + 3) + 1))| + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1cos(1\u03c0((-3((1x - 3)/(-3x)) + 2)/(3((1x - 3)/(-3x)) + 1)) + 2) + 3) - 5 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) = -2sin(1\u03c0(-3|(-2(-1|x + 1| + 3) + 2) + 1|) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-1(-3sin(3\u03c0(4x^2 - 2x - 2) + 3) - 1) + 3) - 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1583", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1(-3cos(3\u03c0(3|x + 1| - 3) - 2) - 2)^2 + 1(-3cos(3\u03c0(3|x + 1| - 3) - 2) - 2)) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0(-5((2(2|x - 3| - 1) - 1)/(-2(2|x - 3| - 1)))^2 - 5((2(2|x - 3| - 1) - 1)/(-2(2|x - 3| - 1))) + 4) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(5(3sin(1\u03c0(3x + 5) + 3) - 2) + 4) - 4 equals zero.\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|(3|(1|(-4x - 4)| + 1) - 3| - 3) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(2sin(2\u03c0((2((-1x)/(-2x + 3)) + 3)/(1((-1x)/(-2x + 3)) + 2)) + 3) - 1) + 1)/(3(2sin(2\u03c0((2((-1x)/(-2x + 3)) + 3)/(1((-1x)/(-2x + 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": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1|(-3(3cos(1\u03c0x - 2) - 1)^2 - 5(3cos(1\u03c0x - 2) - 1) - 4) + 2| - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(3(2sin(2\u03c0(-5x) + 1) - 2)^2 + 2(2sin(2\u03c0(-5x) + 1) - 2))^2 - 2(3(2sin(2\u03c0(-5x) + 1) - 2)^2 + 2(2sin(2\u03c0(-5x) + 1) - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "299", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(4(-1cos(2\u03c0(3|x - 1| + 1) - 3))^2 - 1(-1cos(2\u03c0(3|x - 1| + 1) - 3)) - 2)^2 + 5(4(-1cos(2\u03c0(3|x - 1| + 1) - 3))^2 - 1(-1cos(2\u03c0(3|x - 1| + 1) - 3)) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(4(4(-3x + 2)^2 + 2(-3x + 2) - 1) - 2) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1288", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-4(1|(-5x + 2) - 3| - 1)^2 + 1(1|(-5x + 2) - 3| - 1) - 2) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1148", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(5(-4(-1|x - 3| + 1) - 2) + 1) - 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-5(2sin(1\u03c0(2|x - 3| - 3) + 3) - 2) - 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) = (2(-1(-3cos(2\u03c0((3x + 3)/(2x + 1)) + 2) - 3) - 3) - 2)/(-1(-1(-3cos(2\u03c0((3x + 3)/(2x + 1)) + 2) - 3) - 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-5(2(-1|x + 3| + 3) + 5)^2 + 2(2(-1|x + 3| + 3) + 5) + 2) - 3)/(2(-5(2(-1|x + 3| + 3) + 5)^2 + 2(2(-1|x + 3| + 3) + 5) + 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(5(3(2x - 4) + 4) + 4) - 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "297", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-1|(2|(-3|x + 2|) + 1| + 1) - 3| + 3)^2 - 2(-1|(2|(-3|x + 2|) + 1| + 1) - 3| + 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|((3(1|(-3|x + 2| + 3) + 3| + 1) - 3)/(-2(1|(-3|x + 2| + 3) + 3| + 1) + 3)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2sin(1\u03c0((2((2x)/(-1x - 2)) - 2)/(-1((2x)/(-1x - 2)) - 1)) - 3))^2 - 5(-2sin(1\u03c0((2((2x)/(-1x - 2)) - 2)/(-1((2x)/(-1x - 2)) - 1)) - 3)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "124", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4((-1((-2(2|x + 1| - 3) - 3)/(-2(2|x + 1| - 3) - 1)) - 1)/(2((-2(2|x + 1| - 3) - 3)/(-2(2|x + 1| - 3) - 1))))^2 - 1((-1((-2(2|x + 1| - 3) - 3)/(-2(2|x + 1| - 3) - 1)) - 1)/(2((-2(2|x + 1| - 3) - 3)/(-2(2|x + 1| - 3) - 1)))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(2|(-2sin(2\u03c0(2x^2 + 5) - 3) - 3) + 1| + 1)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "664", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-5(-2sin(2\u03c0(-2x - 2)) + 3)^2 - 1(-2sin(2\u03c0(-2x - 2)) + 3) + 5) - 2)/(3(-5(-2sin(2\u03c0(-2x - 2)) + 3)^2 - 1(-2sin(2\u03c0(-2x - 2)) + 3) + 5) + 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 (-3(2(1(-2cos(3\u03c0x + 3) - 2) + 5) - 1) + 3)/(3(2(1(-2cos(3\u03c0x + 3) - 2) + 5) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-1(3sin(2\u03c0(5x + 1) + 2) - 2)^2 + 3(3sin(2\u03c0(5x + 1) + 2) - 2) - 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(4(1|((1x - 1)/(3x - 1))| - 1)^2 - 2(1|((1x - 1)/(3x - 1))| - 1) - 5))/(-1(4(1|((1x - 1)/(3x - 1))| - 1)^2 - 2(1|((1x - 1)/(3x - 1))| - 1) - 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(2\u03c0(3|(2|((1x + 1)/(-1x + 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": "199", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(2sin(3\u03c0(1|((2x + 2)/(2x + 3)) + 1| - 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": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2cos(2\u03c0(-2(3|x - 2|) - 3) + 1) - 2))/(3(2cos(2\u03c0(-2(3|x - 2|) - 3) + 1) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(-3(-3|(-3x + 1)|)^2 - 4(-3|(-3x + 1)|) - 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1354", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(3sin(1\u03c0((-3(5x^2 + 4x))/(1(5x^2 + 4x) - 2)))) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(2|(-1(-1x + 3)^2 - 3(-1x + 3) + 5)| + 2) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0((1(-3(2x - 3) - 5) + 2)/(2(-3(2x - 3) - 5))) + 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((3(-3(-1|x - 3| + 2)^2 - 5(-1|x - 3| + 2) - 1) - 2)/(2(-3(-1|x - 3| + 2)^2 - 5(-1|x - 3| + 2) - 1) + 1)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-2(3(-1sin(3\u03c0x + 2) + 1)^2 - 3(-1sin(3\u03c0x + 2) + 1) - 1) + 2)^2 - 5(-2(3(-1sin(3\u03c0x + 2) + 1)^2 - 3(-1sin(3\u03c0x + 2) + 1) - 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-3(-2(3sin(3\u03c0x - 3) - 1)^2 - 3(3sin(3\u03c0x - 3) - 1) - 1))| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(-4(1(-1|x + 1| - 2)^2 + 3(-1|x + 1| - 2) + 2)^2 + 5(1(-1|x + 1| - 2)^2 + 3(-1|x + 1| - 2) + 2) + 5) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1225", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((2(5((3x)/(-3x - 1))^2 - 1((3x)/(-3x - 1)) - 4))/(2(5((3x)/(-3x - 1))^2 - 1((3x)/(-3x - 1)) - 4) + 2))^2 + 1((2(5((3x)/(-3x - 1))^2 - 1((3x)/(-3x - 1)) - 4))/(2(5((3x)/(-3x - 1))^2 - 1((3x)/(-3x - 1)) - 4) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(5(5(-4x^2 + 4x - 5)^2 + 4(-4x^2 + 4x - 5)) - 3) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "533", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-1sin(3\u03c0(-5(2|x + 3| + 1)^2 + 5(2|x + 3| + 1) - 1) + 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1530", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2|(1(-4x + 1)^2 + 1(-4x + 1) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2cos(2\u03c0(-1(1x^2 + 5x + 5)^2 - 5(1x^2 + 5x + 5) - 5) + 3) - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "989", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-5(1(1x^2 + 4x + 1) - 5) + 5)^2 - 2(-5(1(1x^2 + 4x + 1) - 5) + 5) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(4(-4(1sin(2\u03c0x + 2) - 2) - 5) - 3) - 3 = 0 have in the range [-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) = 2(1cos(1\u03c0(3|(-3x + 4)| - 3) - 2) + 3)^2 - 3(1cos(1\u03c0(3|(-3x + 4)| - 3) - 2) + 3) - 3 where -10 \u2264 x \u2264 10.\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 (1(5(-5(1x + 5)^2 + 5(1x + 5) + 4)^2 - 1(-5(1x + 5)^2 + 5(1x + 5) + 4) - 2))/(1(5(-5(1x + 5)^2 + 5(1x + 5) + 4)^2 - 1(-5(1x + 5)^2 + 5(1x + 5) + 4) - 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2|(-2(4x^2 - 1x - 5)^2 + 5(4x^2 - 1x - 5) + 5) - 1| - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(3cos(3\u03c0(1(-2|x + 2| + 3) + 5) - 2) + 2) + 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-1|(-3sin(3\u03c0(-3x - 2) + 1)) + 3| + 3) + 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-3|(2|(1|x| + 1) - 2| - 3) - 2| - 3) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-3(2sin(3\u03c0(3x^2 - 2x - 3) + 3) - 1)^2 + 2(2sin(3\u03c0(3x^2 - 2x - 3) + 3) - 1) + 1) - 1)/(-2(-3(2sin(3\u03c0(3x^2 - 2x - 3) + 3) - 1)^2 + 2(2sin(3\u03c0(3x^2 - 2x - 3) + 3) - 1) + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1183", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((2(3cos(3\u03c0(-4x^2 + 1x + 2) + 1)) - 2)/(1(3cos(3\u03c0(-4x^2 + 1x + 2) + 1)) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1546", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(3(1|(3x - 3) + 3| - 3)^2 - 2(1|(3x - 3) + 3| - 3) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(3\u03c0(-5(3|(-5x^2 + 1x - 2)| + 1) - 4) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1256", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(3|(2(-4x^2 - 4x + 5)^2 + 5(-4x^2 - 4x + 5) - 1)| + 3) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "935", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3(-2(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 5) - 4) + 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(2((1(-4x + 2) - 1)/(-3(-4x + 2)))^2 - 5((1(-4x + 2) - 1)/(-3(-4x + 2))) - 3) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((-1(2|(2x^2 + 3x - 3) - 2| - 2) + 3)/(-2(2|(2x^2 + 3x - 3) - 2| - 2) + 3)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(1(-2|(-3|x - 3| + 1) - 1| + 1) + 5) - 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(-2(1(-5x - 4) + 1)^2 - 2(1(-5x - 4) + 1) - 1) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1515", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1((-2(3cos(2\u03c0((-1x + 2)/(-1x - 2)) - 2)) + 3)/(3(3cos(2\u03c0((-1x + 2)/(-1x - 2)) - 2)) + 1)))/(-2((-2(3cos(2\u03c0((-1x + 2)/(-1x - 2)) - 2)) + 3)/(3(3cos(2\u03c0((-1x + 2)/(-1x - 2)) - 2)) + 1)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-1|(2(-1x^2 - 5x - 5)^2 - 4) + 1| + 2) + 3)/(1(-1|(2(-1x^2 - 5x - 5)^2 - 4) + 1| + 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(-3|(1((1x + 2)/(2x - 3)))| - 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "69", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(-3|(-4(-5x^2 - 3x - 2) + 1) + 3| - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1567", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-3(2(1x - 5)^2 - 4) - 4) + 3| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-1((-3(2sin(3\u03c0x + 3) + 2) - 3)/(2(2sin(3\u03c0x + 3) + 2)))^2 - 3((-3(2sin(3\u03c0x + 3) + 2) - 3)/(2(2sin(3\u03c0x + 3) + 2))) + 2) + 3)/(2(-1((-3(2sin(3\u03c0x + 3) + 2) - 3)/(2(2sin(3\u03c0x + 3) + 2)))^2 - 3((-3(2sin(3\u03c0x + 3) + 2) - 3)/(2(2sin(3\u03c0x + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3((-1(-1(1x^2 - 3x - 5)^2 - 5(1x^2 - 3x - 5) + 3) - 2)/(-3(-1(1x^2 - 3x - 5)^2 - 5(1x^2 - 3x - 5) + 3))) - 2)/(-2((-1(-1(1x^2 - 3x - 5)^2 - 5(1x^2 - 3x - 5) + 3) - 2)/(-3(-1(1x^2 - 3x - 5)^2 - 5(1x^2 - 3x - 5) + 3))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0(3|(-3|((-2x + 3)/(3x)) + 2| - 2) - 2| + 3) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(2(1|(5x^2 - 4x - 5) + 2|) + 1)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1136", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-1(3|(-3sin(2\u03c0x + 1) - 1)| - 2)^2 + 5(3|(-3sin(2\u03c0x + 1) - 1)| - 2) - 5) - 2)/(2(-1(3|(-3sin(2\u03c0x + 1) - 1)| - 2)^2 + 5(3|(-3sin(2\u03c0x + 1) - 1)| - 2) - 5) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "116", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1|(3|(-3sin(3\u03c0x + 1) + 2) + 2|) - 3| + 2)^2 - 3(-1|(3|(-3sin(3\u03c0x + 1) + 2) + 2|) - 3| + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0(-3(4(-3|x - 2|) + 4) + 5)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0((1(-5(-3x - 2)^2 - 4(-3x - 2) - 3))/(1(-5(-3x - 2)^2 - 4(-3x - 2) - 3) + 2)) - 3) equals zero.\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) = 3sin(2\u03c0(5(-5((-2x)/(2x + 2))^2 + 3((-2x)/(2x + 2)))^2 - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1158", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2((3(-1|(-4x^2 + 4x + 5) + 3| + 3) + 3)/(3(-1|(-4x^2 + 4x + 5) + 3| + 3) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-1((2(2x^2 - 4x - 3) + 3)/(3(2x^2 - 4x - 3)))^2 - 1((2(2x^2 - 4x - 3) + 3)/(3(2x^2 - 4x - 3))) + 4) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(2|(-4(-5x^2 + 2x + 5) + 4) - 2| - 3)^2 + 5(2|(-4(-5x^2 + 2x + 5) + 4) - 2| - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-1sin(1\u03c0(-1|((-1x)/(-1x + 2)) - 2|) + 3)) + 1)/(-2(-1sin(1\u03c0(-1|((-1x)/(-1x + 2)) - 2|) + 3)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2((1(-1|(3sin(3\u03c0x - 3) + 1) + 2| + 2) - 1)/(-3(-1|(3sin(3\u03c0x - 3) + 1) + 2| + 2) + 4)) - 1)/(1((1(-1|(3sin(3\u03c0x - 3) + 1) + 2| + 2) - 1)/(-3(-1|(3sin(3\u03c0x - 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": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(2|(3|(2sin(2\u03c0x))| - 3)| + 3) - 3| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(5(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2)^2 + 1(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2) - 3)^2 + 5(5(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2)^2 + 1(-3sin(3\u03c0(2x^2 - 4x + 1) + 1) + 2) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "380", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(2\u03c0(-4(-1|((-1x - 2)/(2x + 1)) - 3| + 2) + 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(2cos(1\u03c0((-3((-3x + 3)/(-1x + 3)))/(2((-3x + 3)/(-1x + 3)) - 1)) - 1) + 2) - 3)/(-2(2cos(1\u03c0((-3((-3x + 3)/(-1x + 3)))/(2((-3x + 3)/(-1x + 3)) - 1)) - 1) + 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(2\u03c0(1|(-2|(-2x^2 + 2x + 2) + 3| - 3) + 3|) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1376", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(1(1(-1x + 4) + 1)^2 - 5(1(-1x + 4) + 1) + 2)^2 - 2(1(1(-1x + 4) + 1)^2 - 5(1(-1x + 4) + 1) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-1|(-3cos(3\u03c0(-2|x + 3| + 1) - 3) - 2) - 1| + 2) - 1)/(3(-1|(-3cos(3\u03c0(-2|x + 3| + 1) - 3) - 2) - 1| + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1cos(3\u03c0(-4(2|x| + 3)^2 + 5(2|x| + 3) + 1) - 3))^2 - 3(1cos(3\u03c0(-4(2|x| + 3)^2 + 5(2|x| + 3) + 1) - 3)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1393", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(3cos(2\u03c0(-1(-3|x - 2| + 2) - 5) - 1)) - 2)/(-2(3cos(2\u03c0(-1(-3|x - 2| + 2) - 5) - 1)) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3(-1sin(2\u03c0((1x - 3)/(-1x + 2)) - 1))) + 3)/(-1(-3(-1sin(2\u03c0((1x - 3)/(-1x + 2)) - 1)))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0(5((3(-2x - 4) - 2)/(-2(-2x - 4) + 3)) - 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(2|(-1|(5x - 5) + 2| + 2) + 2| - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-2(1(-3cos(2\u03c0x - 2) + 2)) - 2)/(3(1(-3cos(2\u03c0x - 2) + 2)) - 2))^2 + 5((-2(1(-3cos(2\u03c0x - 2) + 2)) - 2)/(3(1(-3cos(2\u03c0x - 2) + 2)) - 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(-2(3cos(3\u03c0x + 2) - 3) - 5) - 1| + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-2|(2|(-1|x - 2| + 1) + 1| - 3)| - 3) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(3\u03c0((2(-1((-1x - 1)/(2x + 3))^2 - 3((-1x - 1)/(2x + 3)) + 5))/(1(-1((-1x - 1)/(2x + 3))^2 - 3((-1x - 1)/(2x + 3)) + 5) + 1)) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-3|((-1((2x + 2)/(1x)) + 3)/(-3((2x + 2)/(1x)) + 2)) + 3| + 2) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(1(-3|(1x^2 - 3x) + 1|)^2 - 4(-3|(1x^2 - 3x) + 1|) - 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(1((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2))^2 - 3((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2)) - 1) + 2)/(-2(1((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2))^2 - 3((-3(2|x - 1| - 3) + 2)/(-1(2|x - 1| - 3) + 2)) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((2(2cos(1\u03c0(-1x - 5) + 2) + 2) - 2)/(3(2cos(1\u03c0(-1x - 5) + 2) + 2) + 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 solutions does the equation -2|(-2sin(1\u03c0(-2((2x + 1)/(2x + 3)) - 5) - 1) + 3)| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-3|(-2|(2cos(3\u03c0x)) + 1| + 2)| + 1)^2 - 5(-3|(-2|(2cos(3\u03c0x)) + 1| + 2)| + 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "340", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-2(-2e^(1(4x^2 + 1x)) + 2) + 3)/(3(-2e^(1(4x^2 + 1x)) + 2) + 1)) - 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(5(2(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) - 5) - 3)^2 - 2(5(2(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) - 5) - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(3(-3sin(1\u03c0((1x)/(-3x - 2))) + 3)^2 + 3(-3sin(1\u03c0((1x)/(-3x - 2))) + 3) - 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1|(5(-2x^2 + 4) + 1)| - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(4(2(-2cos(1\u03c0x - 2) - 1)^2 + 2(-2cos(1\u03c0x - 2) - 1) - 1)^2 + 1(2(-2cos(1\u03c0x - 2) - 1)^2 + 2(-2cos(1\u03c0x - 2) - 1) - 1) - 2))/(1(4(2(-2cos(1\u03c0x - 2) - 1)^2 + 2(-2cos(1\u03c0x - 2) - 1) - 1)^2 + 1(2(-2cos(1\u03c0x - 2) - 1)^2 + 2(-2cos(1\u03c0x - 2) - 1) - 1) - 2) + 3) 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 5(-2|(1((1x)/(2x - 1))^2 + 1((1x)/(2x - 1))) - 1|) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-4(2(2|x - 3| - 1)^2 - 4(2|x - 3| - 1) - 2)^2 + 5(2(2|x - 3| - 1)^2 - 4(2|x - 3| - 1) - 2) + 4) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(5(-5((2x + 1)/(1x))^2 - 5((2x + 1)/(1x)) + 5)^2 - 1(-5((2x + 1)/(1x))^2 - 5((2x + 1)/(1x)) + 5) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(1\u03c0(2(2(1|x + 2| + 1)^2 - 5(1|x + 2| + 1) - 3) + 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "363", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4((3(-3cos(2\u03c0(-2x + 2) - 2) - 3))/(2(-3cos(2\u03c0(-2x + 2) - 2) - 3) - 1)) - 5 = 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": "Determine the number of values x in [-10, 10] where f(x) = 1(3((-2(2sin(3\u03c0x - 2) + 3))/(-1(2sin(3\u03c0x - 2) + 3) - 2))^2 + 1((-2(2sin(3\u03c0x - 2) + 3))/(-1(2sin(3\u03c0x - 2) + 3) - 2)) + 1)^2 - 5(3((-2(2sin(3\u03c0x - 2) + 3))/(-1(2sin(3\u03c0x - 2) + 3) - 2))^2 + 1((-2(2sin(3\u03c0x - 2) + 3))/(-1(2sin(3\u03c0x - 2) + 3) - 2)) + 1) + 1 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) = -4(2sin(2\u03c0(-5((3x - 1)/(-3x - 1)) + 2) + 1) - 2)^2 + 1(2sin(2\u03c0(-5((3x - 1)/(-3x - 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": "72", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(2|(1((2x - 1)/(2x))^2 - 4((2x - 1)/(2x)) - 2) + 1| - 3)) + 2 = 0 have in the range [-10, 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) = -2sin(2\u03c0(-3(2|(3x^2 - 1x - 5) - 1| + 1)^2 - 3(2|(3x^2 - 1x - 5) - 1| + 1) + 5) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "622", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-4(-3cos(3\u03c0((3x - 1)/(-3x - 1)) + 1)) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "52", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1|((-1(3x - 4) - 3)/(-3(3x - 4))) + 1| - 1) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-2|(-1(-3|x - 3| - 1)^2 - 4(-3|x - 3| - 1))| - 1)^2 + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|((3((-3(-1x^2 + 5x + 5) - 1)/(1(-1x^2 + 5x + 5) + 3)) - 1)/(-3((-3(-1x^2 + 5x + 5) - 1)/(1(-1x^2 + 5x + 5) + 3)) + 4))| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(1(-3cos(3\u03c0(1x^2 + 1) - 2) - 2)^2 - 3(-3cos(3\u03c0(1x^2 + 1) - 2) - 2) - 4) + 1)/(-1(1(-3cos(3\u03c0(1x^2 + 1) - 2) - 2)^2 - 3(-3cos(3\u03c0(1x^2 + 1) - 2) - 2) - 4) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "392", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(4(-1(4x - 1) + 4)^2 - 2(-1(4x - 1) + 4) - 4)^2 + 1(4(-1(4x - 1) + 4)^2 - 2(-1(4x - 1) + 4) - 4) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(3(-4(-3|x| - 2) - 5) - 1) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((-1(-1(2cos(1\u03c0x - 1) + 3)^2 + 3(2cos(1\u03c0x - 1) + 3) + 2) - 3)/(-3(-1(2cos(1\u03c0x - 1) + 3)^2 + 3(2cos(1\u03c0x - 1) + 3) + 2) + 4))^2 + 2((-1(-1(2cos(1\u03c0x - 1) + 3)^2 + 3(2cos(1\u03c0x - 1) + 3) + 2) - 3)/(-3(-1(2cos(1\u03c0x - 1) + 3)^2 + 3(2cos(1\u03c0x - 1) + 3) + 2) + 4)) - 5 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": "How many zeros does the function f(x) = (-1(1sin(3\u03c0((3(5x - 4) - 2)/(3(5x - 4) - 1)) + 1) - 3) - 2)/(-2(1sin(3\u03c0((3(5x - 4) - 2)/(3(5x - 4) - 1)) + 1) - 3) - 2) have in the interval [-10, 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) = 1(1(1((2x - 1)/(-2x + 3)) - 2)^2 - 4(1((2x - 1)/(-2x + 3)) - 2) + 2)^2 - 2(1(1((2x - 1)/(-2x + 3)) - 2)^2 - 4(1((2x - 1)/(-2x + 3)) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2((-2(2cos(3\u03c0((3x - 3)/(2x + 1)) - 3)) - 3)/(-2(2cos(3\u03c0((3x - 3)/(2x + 1)) - 3)) - 1)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(2(2e^(-1(-2|x + 1| + 2)) - 3) - 1) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-2|(-2|(2x - 2) + 1| + 2) + 1| + 2) + 2)/(3(-2|(-2|(2x - 2) + 1| + 2) + 1| + 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-2cos(2\u03c0(3(5x + 1)) + 3) - 2)^2 + 5(-2cos(2\u03c0(3(5x + 1)) + 3) - 2) + 2 = 0 have in the range [-10, 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 2cos(1\u03c0((-1(-4(-2|x + 3| + 2) + 3) + 1)/(2(-4(-2|x + 3| + 2) + 3) - 1)) + 2) + 1 = 0 have in the range [-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(5(3cos(1\u03c0(2x - 5)) + 1) + 5) - 3)/(-2(5(3cos(1\u03c0(2x - 5)) + 1) + 5) + 3) 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 solutions does the equation -2|(-1(3sin(1\u03c0(-3|x| - 2)) - 2)^2 + 2(3sin(1\u03c0(-3|x| - 2)) - 2) - 1) + 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-3(3|(3|x + 1| - 3)| - 1) + 4)^2 + 4(-3(3|(3|x + 1| - 3)| - 1) + 4) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-5(3cos(2\u03c0(-3x - 5) - 2) + 2) + 4)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1(2sin(3\u03c0((-1x + 3)/(-3x - 1)) + 1) - 3) + 5) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(5(-3|(2x - 1) - 2|)^2 - 1(-3|(2x - 1) - 2|) + 2) + 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1239", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(2(-2(3|x - 3| - 2)^2 - 4(3|x - 3| - 2) + 4)^2 + 1(-2(3|x - 3| - 2)^2 - 4(3|x - 3| - 2) + 4) + 2) - 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "594", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-4(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2)^2 + 2(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2) + 1)^2 + 2(-4(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2)^2 + 2(5((-2x - 1)/(1x + 2))^2 + 4((-2x - 1)/(1x + 2)) - 2) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(3\u03c0((-3(-1|(1x - 1) - 1| - 1) + 2)/(3(-1|(1x - 1) - 1| - 1) + 3)) + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-3|((2(1x^2 - 5x - 2) + 3)/(1(1x^2 - 5x - 2) + 1)) - 3| + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-4((1(-2cos(2\u03c0x) - 3) + 1)/(-3(-2cos(2\u03c0x) - 3) + 1)) + 1) + 2)/(1(-4((1(-2cos(2\u03c0x) - 3) + 1)/(-3(-2cos(2\u03c0x) - 3) + 1)) + 1) - 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) = (1((1(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) - 3)/(-3(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) + 2)) + 1)/(1((1(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) - 3)/(-3(4(4x^2 - 3x - 1)^2 - 1(4x^2 - 3x - 1) - 4) + 2)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(2sin(3\u03c0(-1|(-2x^2 + 4x - 5) - 1|) + 1) - 1)^2 - 2(2sin(3\u03c0(-1|(-2x^2 + 4x - 5) - 1|) + 1) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1425", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-2(1|(-1e^(-1x) + 1) + 1|) + 2)^2 - 2(-2(1|(-1e^(-1x) + 1) + 1|) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(1(-1sin(2\u03c0(3x^2 + 2x + 2) + 3) + 1)^2 + 4(-1sin(2\u03c0(3x^2 + 2x + 2) + 3) + 1) - 4) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1150", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(3|((-3(-1x^2 - 5x - 1) + 2)/(-3(-1x^2 - 5x - 1))) + 3| + 1) + 1) + 3 = 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 zeros does the function f(x) = 1(-1|((-3(-1x^2 - 4x + 5) - 3)/(-3(-1x^2 - 4x + 5) + 2)) - 1| - 1)^2 + 2(-1|((-3(-1x^2 - 4x + 5) - 3)/(-3(-1x^2 - 4x + 5) + 2)) - 1| - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(1\u03c0(2(-3|(2|x - 2| + 2) - 2| + 2) - 1) - 3) = 0 have in the range [-10, 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 -2sin(1\u03c0((3(-2|(4x^2 - 3x + 1) + 3| + 3) + 1)/(1(-2|(4x^2 - 3x + 1) + 3| + 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": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(3\u03c0(3(-1|((2x + 3)/(3x - 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": "121", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5((-2((-2(-3cos(2\u03c0x - 1) + 2) + 1)/(-1(-3cos(2\u03c0x - 1) + 2) + 3)) + 2)/(2((-2(-3cos(2\u03c0x - 1) + 2) + 1)/(-1(-3cos(2\u03c0x - 1) + 2) + 3)) + 3)) - 5 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": "How many zeros does the function f(x) = -2|(-3(3(1x^2 + 4x + 5)^2 - 4(1x^2 + 4x + 5) - 1)^2 - 5(3(1x^2 + 4x + 5)^2 - 4(1x^2 + 4x + 5) - 1) + 2)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(2|(4(1x)^2 + 2(1x) - 3) + 2| + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1634", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-4(-3sin(3\u03c0(1x - 3) - 2))^2 - 5(-3sin(3\u03c0(1x - 3) - 2)) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0((2((-3((-1x + 1)/(-1x + 2)) - 1)/(-3((-1x + 1)/(-1x + 2)))) + 3)/(-3((-3((-1x + 1)/(-1x + 2)) - 1)/(-3((-1x + 1)/(-1x + 2)))))) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(4(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1)^2 - 1(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1) - 2)^2 - 1(4(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1)^2 - 1(-2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) + 1) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-1sin(2\u03c0((3((-1x + 3)/(-2x - 3)))/(2((-1x + 3)/(-2x - 3)) - 1))) + 1)^2 - 1(-1sin(2\u03c0((3((-1x + 3)/(-2x - 3)))/(2((-1x + 3)/(-2x - 3)) - 1))) + 1) - 1 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": "Find the number of x-intercepts of the function f(x) = 2|(-1|(1(5x^2 - 3x)^2 - 3(5x^2 - 3x) - 1) - 1| + 3)| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(3cos(2\u03c0((2(1|x + 3|) - 3)/(-3(1|x + 3|) - 1)) - 3) - 2) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((-3(-5(3sin(2\u03c0x + 2) + 3)^2 + 4(3sin(2\u03c0x + 2) + 3) + 1) - 1)/(1(-5(3sin(2\u03c0x + 2) + 3)^2 + 4(3sin(2\u03c0x + 2) + 3) + 1) + 3)) + 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": "How many solutions does the equation -3sin(1\u03c0(1((1(-1|x - 3| + 2) + 3)/(-1(-1|x - 3| + 2) - 1))^2 - 2((1(-1|x - 3| + 2) + 3)/(-1(-1|x - 3| + 2) - 1)) - 5)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "226", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(1(-2cos(1\u03c0((-3x)/(3x - 2))))^2 + 4(-2cos(1\u03c0((-3x)/(3x - 2)))) - 4) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(2cos(2\u03c0((-2(2|x - 3| - 1) - 1)/(3(2|x - 3| - 1) + 1)) + 3) + 2) - 2)/(1(2cos(2\u03c0((-2(2|x - 3| - 1) - 1)/(3(2|x - 3| - 1) + 1)) + 3) + 2) - 3) = 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": "Determine the number of values x in [-10, 10] where f(x) = 2(-5(5(1e^(1x)) - 1)^2 - 1(5(1e^(1x)) - 1) + 2)^2 - 3(-5(5(1e^(1x)) - 1)^2 - 1(5(1e^(1x)) - 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3cos(1\u03c0(-1(5x^2 + 1)^2 + 5(5x^2 + 1) - 3) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "979", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-3(1(1x^2 + 5x + 1) - 2)^2 + 4(1(1x^2 + 5x + 1) - 2) + 5)^2 + 2(-3(1(1x^2 + 5x + 1) - 2)^2 + 4(1(1x^2 + 5x + 1) - 2) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(3|((3(2sin(1\u03c0x + 3)) - 3)/(3(2sin(1\u03c0x + 3)))) + 1| - 2)^2 - 2(3|((3(2sin(1\u03c0x + 3)) - 3)/(3(2sin(1\u03c0x + 3)))) + 1| - 2) - 5 = 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 zeros does the function f(x) = 4((-2(-3cos(3\u03c0(2x + 3) + 3)) + 1)/(-2(-3cos(3\u03c0(2x + 3) + 3)) - 3))^2 + 5((-2(-3cos(3\u03c0(2x + 3) + 3)) + 1)/(-2(-3cos(3\u03c0(2x + 3) + 3)) - 3)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((3(1sin(3\u03c0((-3x + 1)/(2x + 3)))) + 1)/(1(1sin(3\u03c0((-3x + 1)/(2x + 3)))) + 1)) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(3(-4(5x + 4)^2 - 4)^2 - 4(-4(5x + 4)^2 - 4) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "338", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(1|(-3(4x + 5)^2 + 1(4x + 5) + 3) + 3| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1574", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(3sin(3\u03c0((2(-3x - 4) - 2)/(1(-3x - 4)))) + 3)^2 + 1(3sin(3\u03c0((2(-3x - 4) - 2)/(1(-3x - 4)))) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(-3(-2|(1x + 3) - 3| + 2) + 1) + 2) + 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) = -3(1|(-3(-1x + 3)^2 + 3(-1x + 3) + 4) - 2| - 3)^2 - 3(1|(-3(-1x + 3)^2 + 3(-1x + 3) + 4) - 2| - 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(-4(-3(1|x - 2| + 3)) - 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3sin(1\u03c0(5(-3|x - 3| + 1) + 3) + 3) + 1)^2 - 5(3sin(1\u03c0(5(-3|x - 3| + 1) + 3) + 3) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "298", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2sin(3\u03c0(3((1x - 3)/(1x + 1))^2 + 4((1x - 3)/(1x + 1)) - 5) - 3) + 3)^2 - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "297", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(5(5(-1|x| + 1) + 3)^2 + 2(5(-1|x| + 1) + 3) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(3|((-2(-1x + 2) - 1)/(1(-1x + 2) - 2))| + 2) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "137", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(1(3cos(2\u03c0((3x + 1)/(3x - 2)) - 2) - 3)^2 + 2(3cos(2\u03c0((3x + 1)/(3x - 2)) - 2) - 3) - 2) + 2)/(2(1(3cos(2\u03c0((3x + 1)/(3x - 2)) - 2) - 3)^2 + 2(3cos(2\u03c0((3x + 1)/(3x - 2)) - 2) - 3) - 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((-2(-2(-1x^2 - 4x + 5) - 1) - 3)/(2(-2(-1x^2 - 4x + 5) - 1) + 1))^2 - 2((-2(-2(-1x^2 - 4x + 5) - 1) - 3)/(2(-2(-1x^2 - 4x + 5) - 1) + 1)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-5((-3(-5x^2 + 5) + 1)/(-3(-5x^2 + 5)))^2 - 3((-3(-5x^2 + 5) + 1)/(-3(-5x^2 + 5))) + 5) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(5(-3|((-2x + 1)/(-2x - 3)) + 1| + 1)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-1(1(-3cos(3\u03c0x) - 2)^2 - 2(-3cos(3\u03c0x) - 2) - 4) + 1)/(-2(1(-3cos(3\u03c0x) - 2)^2 - 2(-3cos(3\u03c0x) - 2) - 4) + 3)) + 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 zeros does the function f(x) = -1cos(3\u03c0((-1(2(1x - 1) + 1) + 1)/(-2(2(1x - 1) + 1) + 3)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-4(3sin(3\u03c0(-3x^2 + 5x + 2) + 3) + 1) + 3)^2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1152", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-2cos(3\u03c0(2(-3|x + 2|) - 4) - 2) - 2) + 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1((-3(2(-2x^2 - 5x + 1) + 3) - 3)/(2(2(-2x^2 - 5x + 1) + 3) + 1))^2 + 1((-3(2(-2x^2 - 5x + 1) + 3) - 3)/(2(2(-2x^2 - 5x + 1) + 3) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(3(-3((-1x - 1)/(-2x + 3)) - 5) - 2) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-4(1sin(3\u03c0(4x^2 + 4) - 3))^2 - 5(1sin(3\u03c0(4x^2 + 4) - 3)) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "554", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(4(-4(-5x^2 + 3x + 1) + 4) + 2)^2 + 2(4(-4(-5x^2 + 3x + 1) + 4) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3|(-1|((-1x + 3)/(3x - 1))| + 3)| + 1) - 1)/(3(-3|(-1|((-1x + 3)/(3x - 1))| + 3)| + 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2cos(3\u03c0(4((3x + 2)/(-1x + 2))^2 + 1((3x + 2)/(-1x + 2)) + 4) - 3) + 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(3|(-2(-1x^2 + 5x + 1)^2 - 4(-1x^2 + 5x + 1) + 2)| - 3)| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-1e^(-2(-2|(-1x^2 - 4x - 5) + 3| + 1)) + 2))/(-2(-1e^(-2(-2|(-1x^2 - 4x - 5) + 3| + 1)) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2e^(1(-3((-1(3|x + 1| - 2) + 3)/(2(3|x + 1| - 2) - 1))^2 + 5)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0((3(-4(2x)^2 - 2(2x) - 1) - 3)/(1(-4(2x)^2 - 2(2x) - 1) + 1)) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(2|(3|(-3cos(2\u03c0x + 2) - 1) + 1|) + 1| - 3)^2 - 5(2|(3|(-3cos(2\u03c0x + 2) - 1) + 1|) + 1| - 3) + 1 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": "Find the number of x-intercepts of the function f(x) = -5(1(-3(4x^2 - 1x - 1)^2 + 3(4x^2 - 1x - 1) - 5) + 5)^2 - 5(1(-3(4x^2 - 1x - 1)^2 + 3(4x^2 - 1x - 1) - 5) + 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(5(-3sin(3\u03c0(4x^2 + 5x + 5)) + 1)^2 - 1(-3sin(3\u03c0(4x^2 + 5x + 5)) + 1) - 3) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "456", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3sin(2\u03c0(3((-3x + 2)/(-2x + 3))^2 - 2((-3x + 2)/(-2x + 3)) - 3) - 2) + 1)^2 - 5(-3sin(2\u03c0(3((-3x + 2)/(-2x + 3))^2 - 2((-3x + 2)/(-2x + 3)) - 3) - 2) + 1) + 2 = 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((1(-2(1|x + 3| - 2)^2 + 1(1|x + 3| - 2) + 5) + 2)/(1(-2(1|x + 3| - 2)^2 + 1(1|x + 3| - 2) + 5) + 3))^2 + 2((1(-2(1|x + 3| - 2)^2 + 1(1|x + 3| - 2) + 5) + 2)/(1(-2(1|x + 3| - 2)^2 + 1(1|x + 3| - 2) + 5) + 3)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-2((3(3|x - 3| - 2) + 2)/(-2(3|x - 3| - 2) - 3)) + 3)/(3((3(3|x - 3| - 2) + 2)/(-2(3|x - 3| - 2) - 3)) - 1))^2 - 3((-2((3(3|x - 3| - 2) + 2)/(-2(3|x - 3| - 2) - 3)) + 3)/(3((3(3|x - 3| - 2) + 2)/(-2(3|x - 3| - 2) - 3)) - 1)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-2cos(1\u03c0(-2|(-2|x|) - 3| + 2) - 3)) - 3)/(2(-2cos(1\u03c0(-2|(-2|x|) - 3| + 2) - 3)) + 1) equals zero.\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 -4(4(2|(-5x^2 + 5x - 1) + 2| - 1) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1|(-3cos(3\u03c0((2x + 3)/(3x - 2)) + 1) - 3) + 3| + 2) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0((-2((2(-2x^2 + 4x + 5) + 2)/(-3(-2x^2 + 4x + 5) + 2)) + 3)/(1((2(-2x^2 + 4x + 5) + 2)/(-3(-2x^2 + 4x + 5) + 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": "190", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1(2|(3|x - 1| - 3)| - 1)^2 + 2(2|(3|x - 1| - 3)| - 1) + 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(1sin(3\u03c0(1|(1x^2 - 1x - 4) - 1| + 3) + 2) - 1)^2 - 3(1sin(3\u03c0(1|(1x^2 - 1x - 4) - 1| + 3) + 2) - 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "602", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(3(-4(-1x + 5)^2 + 3(-1x + 5) + 3) - 5) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1100", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2|(1|(1x + 3) + 2| - 3) - 2| - 2)^2 + 1(2|(1|(1x + 3) + 2| - 3) - 2| - 2) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(3(1(1|x - 3| - 2) - 3)^2 + 3(1(1|x - 3| - 2) - 3) + 1)^2 + 2(3(1(1|x - 3| - 2) - 3)^2 + 3(1(1|x - 3| - 2) - 3) + 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1sin(1\u03c0(2(3|x - 3| + 1)) + 3) + 3) - 1| + 3 equals zero.\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 5(5(4(-3x - 3)^2 + 3(-3x - 3) - 4)^2 - 2(4(-3x - 3)^2 + 3(-3x - 3) - 4) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2|((-2(5x^2 + 1x - 5) + 2)/(2(5x^2 + 1x - 5))) + 2| + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-5(-3|(1x - 4) + 2| + 1)^2 - 5(-3|(1x - 4) + 2| + 1) - 1)^2 + 2(-5(-3|(1x - 4) + 2| + 1)^2 - 5(-3|(1x - 4) + 2| + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0(5(1(-3|x - 3| - 1) + 3) - 2) - 1) - 1 equals zero.\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 -1((2(2(-1sin(1\u03c0x + 1) - 3)^2 + 4(-1sin(1\u03c0x + 1) - 3) - 3) - 3)/(1(2(-1sin(1\u03c0x + 1) - 3)^2 + 4(-1sin(1\u03c0x + 1) - 3) - 3) + 2))^2 - 5((2(2(-1sin(1\u03c0x + 1) - 3)^2 + 4(-1sin(1\u03c0x + 1) - 3) - 3) - 3)/(1(2(-1sin(1\u03c0x + 1) - 3)^2 + 4(-1sin(1\u03c0x + 1) - 3) - 3) + 2)) - 1 = 0 have in the range [-10, 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(3|(-1|(2x^2 - 5)| + 2)| - 1) - 1)/(1(3|(-1|(2x^2 - 5)| + 2)| - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-3sin(1\u03c0(2|(-3|x| - 2) + 3| + 1) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3((3(3cos(2\u03c0(5x - 4) + 2) - 2) - 3)/(3(3cos(2\u03c0(5x - 4) + 2) - 2) - 2))^2 + 1((3(3cos(2\u03c0(5x - 4) + 2) - 2) - 3)/(3(3cos(2\u03c0(5x - 4) + 2) - 2) - 2)) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-3cos(1\u03c0(-5((-2x + 2)/(-2x + 3)) - 5) - 2) - 2) + 3 where -10 \u2264 x \u2264 10.\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) = 3|(2cos(2\u03c0(2(-5x - 3)^2 - 2(-5x - 3) - 4))) - 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1276", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(2(-2|(-3|x - 1| + 2) + 1| + 3)^2 - 3(-2|(-3|x - 1| + 2) + 1| + 3) - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(1(2|(-1x^2 + 3x - 2) + 1| + 2)^2 - 5)^2 + 5(1(2|(-1x^2 + 3x - 2) + 1| + 2)^2 - 5) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(-3|(-4(2|x + 3| + 2) - 5) + 2| - 1) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "452", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(1\u03c0(2|(-4(-5x - 2)) - 1| + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "799", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3cos(2\u03c0(-2|(-5x^2 + 2x - 2) + 2| - 2) - 2) - 1)^2 + 3(-3cos(2\u03c0(-2|(-5x^2 + 2x - 2) + 2| - 2) - 2) - 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1226", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-2((2(5x^2 - 4) + 2)/(3(5x^2 - 4) - 2))^2 - 4((2(5x^2 - 4) + 2)/(3(5x^2 - 4) - 2)))^2 + 4(-2((2(5x^2 - 4) + 2)/(3(5x^2 - 4) - 2))^2 - 4((2(5x^2 - 4) + 2)/(3(5x^2 - 4) - 2))) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((-2(1(-4x - 5)^2 + 5(-4x - 5) - 5) + 2)/(-2(1(-4x - 5)^2 + 5(-4x - 5) - 5) + 3))^2 + 3((-2(1(-4x - 5)^2 + 5(-4x - 5) - 5) + 2)/(-2(1(-4x - 5)^2 + 5(-4x - 5) - 5) + 3)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2(-5(-2sin(3\u03c0x - 3) + 1) - 3) + 3) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(1|(-3((-3x - 2)/(-1x + 2))^2 + 5((-3x - 2)/(-1x + 2)) + 2) - 3| - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-5((2(3|x + 3| - 1) - 2)/(-3(3|x + 3| - 1)))^2 + 2((2(3|x + 3| - 1) - 2)/(-3(3|x + 3| - 1))) + 4) - 3)/(1(-5((2(3|x + 3| - 1) - 2)/(-3(3|x + 3| - 1)))^2 + 2((2(3|x + 3| - 1) - 2)/(-3(3|x + 3| - 1))) + 4) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(3|(-1(-3|x| + 3)^2 - 2(-3|x| + 3) + 3) + 2| - 3) - 2)/(1(3|(-1(-3|x| + 3)^2 - 2(-3|x| + 3) + 3) + 2| - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-1((2(-3x^2 + 4x) + 2)/(-3(-3x^2 + 4x) + 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": "64", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2((2(-3cos(2\u03c0x + 1) - 2))/(2(-3cos(2\u03c0x + 1) - 2) - 1)) + 2) - 5 equals zero.\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|(-3cos(3\u03c0((1((1x + 3)/(-3x + 1)) - 3)/(2((1x + 3)/(-3x + 1)) - 3)) + 1) - 2)| + 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": "Determine the number of values x in [-10, 10] where f(x) = -3(-3cos(1\u03c0(2(-1|x + 3| - 2)^2 - 1(-1|x + 3| - 2) + 5) + 1) + 2)^2 + 1(-3cos(1\u03c0(2(-1|x + 3| - 2)^2 - 1(-1|x + 3| - 2) + 5) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "291", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(2|((-2(-1cos(3\u03c0x - 1) - 1))/(2(-1cos(3\u03c0x - 1) - 1) - 1)) + 2| - 2) - 5 = 0 have in the range [-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) = (-2(3(-2cos(1\u03c0(-1|x| + 3) - 1))^2 + 2(-2cos(1\u03c0(-1|x| + 3) - 1)) - 2) - 1)/(-2(3(-2cos(1\u03c0(-1|x| + 3) - 1))^2 + 2(-2cos(1\u03c0(-1|x| + 3) - 1)) - 2) + 3) equals zero.\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) = 2|(-3sin(2\u03c0(2|((-2x - 2)/(2x + 1))| - 2) - 3) + 2) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1((2(-1|x + 1| + 2) + 2)/(2(-1|x + 1| + 2)))^2 - 3((2(-1|x + 1| + 2) + 2)/(2(-1|x + 1| + 2))) - 4) - 2)/(-2(1((2(-1|x + 1| + 2) + 2)/(2(-1|x + 1| + 2)))^2 - 3((2(-1|x + 1| + 2) + 2)/(2(-1|x + 1| + 2))) - 4) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(-2|(4(-4x^2 + 2x - 4) - 5)|) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1198", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3(-3|(-2x^2 - 4x + 2) + 1|) + 5) + 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0((1(-2((-1x - 1)/(-1x))^2 + 1((-1x - 1)/(-1x)) + 2) + 1)/(1(-2((-1x - 1)/(-1x))^2 + 1((-1x - 1)/(-1x)) + 2) + 2))) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(3\u03c0(-1(5((-1x)/(-1x - 2)) + 5) + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "119", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-1sin(2\u03c0(2|((1x - 2)/(-2x - 3)) + 3| - 3) + 1) - 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "97", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-2|(3sin(3\u03c0((-3x + 3)/(-3x - 1)) - 2) + 2) - 1|) - 2)/(1(-2|(3sin(3\u03c0((-3x + 3)/(-3x - 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": "84", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((3((2(1x^2 - 3x - 1) + 1)/(1(1x^2 - 3x - 1) + 2)) + 1)/(2((2(1x^2 - 3x - 1) + 1)/(1(1x^2 - 3x - 1) + 2)) + 2))^2 - 5((3((2(1x^2 - 3x - 1) + 1)/(1(1x^2 - 3x - 1) + 2)) + 1)/(2((2(1x^2 - 3x - 1) + 1)/(1(1x^2 - 3x - 1) + 2)) + 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((2(-1(2|x - 1| - 2)^2 + 4(2|x - 1| - 2) - 4) - 3)/(-2(-1(2|x - 1| - 2)^2 + 4(2|x - 1| - 2) - 4) + 1))^2 + 4((2(-1(2|x - 1| - 2)^2 + 4(2|x - 1| - 2) - 4) - 3)/(-2(-1(2|x - 1| - 2)^2 + 4(2|x - 1| - 2) - 4) + 1)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4((2(1cos(2\u03c0((-1x - 1)/(-1x - 3)) + 1) - 1) + 3)/(-1(1cos(2\u03c0((-1x - 1)/(-1x - 3)) + 1) - 1) - 2))^2 + 1((2(1cos(2\u03c0((-1x - 1)/(-1x - 3)) + 1) - 1) + 3)/(-1(1cos(2\u03c0((-1x - 1)/(-1x - 3)) + 1) - 1) - 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(3\u03c0(2|(2((-2x + 3)/(3x + 3)) - 5) + 1| - 2) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "156", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((2((-2(3cos(2\u03c0x - 3) + 3) + 3)/(-1(3cos(2\u03c0x - 3) + 3) - 1)) + 3)/(3((-2(3cos(2\u03c0x - 3) + 3) + 3)/(-1(3cos(2\u03c0x - 3) + 3) - 1)) + 2)) + 5 equals zero.\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|(-2|(5x^2 + 1x - 1) - 3| + 2) + 2|)^2 - 3(-1|(-2|(5x^2 + 1x - 1) - 3| + 2) + 2|) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3|(-1(-2|x + 2|)^2 + 4(-2|x + 2|) - 1) + 3| + 2) + 3)/(-3(-3|(-1(-2|x + 2|)^2 + 4(-2|x + 2|) - 1) + 3| + 2) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(2|(-2((-3x - 3)/(-3x + 4)) - 5) + 1| - 2)^2 + 4(2|(-2((-3x - 3)/(-3x + 4)) - 5) + 1| - 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2(-2|((2x + 2)/(-2x + 1)) - 2| + 2) + 1)^2 + 3(-2(-2|((2x + 2)/(-2x + 1)) - 2| + 2) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(1(-1sin(1\u03c0((2x - 1)/(3x)) + 2) + 1)^2 + 1(-1sin(1\u03c0((2x - 1)/(3x)) + 2) + 1) - 1) + 2)/(-3(1(-1sin(1\u03c0((2x - 1)/(3x)) + 2) + 1)^2 + 1(-1sin(1\u03c0((2x - 1)/(3x)) + 2) + 1) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-1|(-3(1x^2 - 5x - 3)^2 - 2(1x^2 - 5x - 3) + 1) + 1| + 1) + 1)/(3(-1|(-3(1x^2 - 5x - 3)^2 - 2(1x^2 - 5x - 3) + 1) + 1| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(4(2cos(2\u03c0(-1x - 2) - 2) - 1)^2 - 4(2cos(2\u03c0(-1x - 2) - 2) - 1) + 1) + 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(-3|(-1((2x - 3)/(-2x)) + 2)| + 1)^2 - 4(-3|(-1((2x - 3)/(-2x)) + 2)| + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(2\u03c0(3((2(2x + 3))/(-1(2x + 3) + 2)) + 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(1(2(-3cos(1\u03c0x + 1) + 3) - 3) + 2) - 1)/(-1(1(2(-3cos(1\u03c0x + 1) + 3) - 3) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(3|(-1sin(2\u03c0(-1x^2 - 3x - 4) - 1) + 2) - 3| - 3))/(2(3|(-1sin(2\u03c0(-1x^2 - 3x - 4) - 1) + 2) - 3| - 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5((2(-1|(-3e^(-1x) + 3) + 2| + 2) + 2)/(2(-1|(-3e^(-1x) + 3) + 2| + 2) + 3))^2 - 2((2(-1|(-3e^(-1x) + 3) + 2| + 2) + 2)/(2(-1|(-3e^(-1x) + 3) + 2| + 2) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(5(2|((-3x)/(3x + 2)) + 1| - 3)^2 + 5(2|((-3x)/(3x + 2)) + 1| - 3) - 5) - 3)/(1(5(2|((-3x)/(3x + 2)) + 1| - 3)^2 + 5(2|((-3x)/(3x + 2)) + 1| - 3) - 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1e^(1(1|(-3(3x - 5)^2 - 2(3x - 5) + 3) + 2|)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(-1|((3((-1x + 2)/(3x)) - 2)/(2((-1x + 2)/(3x)) - 1)) - 2| - 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1|((-3(-3|x - 1| + 2) - 3)/(1(-3|x - 1| + 2) - 3)) - 3| + 1)^2 - 2(1|((-3(-3|x - 1| + 2) - 3)/(1(-3|x - 1| + 2) - 3)) - 3| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3cos(1\u03c0(1|(1x^2 - 5x + 4) - 1| + 2) - 1) + 2)^2 - 1(-3cos(1\u03c0(1|(1x^2 - 5x + 4) - 1| + 2) - 1) + 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1(-3|(5x^2 - 1x - 5) - 3| + 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(3|(-2|(4x^2 - 1x - 4) - 3| - 1) + 3| - 2) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(1(2(1|x + 2|) - 5) + 4) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(3cos(1\u03c0(2|(-5x - 3) + 2| - 1) + 2) - 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(3cos(2\u03c0(3(-3x + 3)^2 + 3(-3x + 3) + 5) - 1)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1137", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|(-3sin(1\u03c0(-1x^2 + 3x - 2) + 3) + 1) - 1| + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(1sin(3\u03c0(2(-3|x| + 3)^2 + 5(-3|x| + 3) - 1) - 2) + 2) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1099", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((-2((2(3cos(3\u03c0x + 2) - 1) - 2)/(3(3cos(3\u03c0x + 2) - 1) - 2)) - 1)/(-1((2(3cos(3\u03c0x + 2) - 1) - 2)/(3(3cos(3\u03c0x + 2) - 1) - 2)) - 1)) - 3| - 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) = -5(-1(1((-1x + 2)/(-2x - 1))^2 - 3((-1x + 2)/(-2x - 1)) - 3) - 3)^2 + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(-3((3((1x - 1)/(-3x - 3)) + 1)/(-2((1x - 1)/(-3x - 3)) + 3)) - 1) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0((-3((-3((3x - 2)/(3x)) - 3)/(-2((3x - 2)/(3x)) + 3)) - 3)/(-3((-3((3x - 2)/(3x)) - 3)/(-2((3x - 2)/(3x)) + 3)) - 2)) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1sin(1\u03c0(-1(3x^2 - 3x - 3) + 4) + 1) - 1) + 2)/(-2(1sin(1\u03c0(-1(3x^2 - 3x - 3) + 4) + 1) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2|(-2cos(1\u03c0(-2x^2 - 3) + 2)) + 1| - 1))/(-2(2|(-2cos(1\u03c0(-2x^2 - 3) + 2)) + 1| - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "688", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3((-2(5(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1))/(1(5(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1) + 3)) + 1)/(-1((-2(5(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1))/(1(5(2|x + 3| - 2)^2 - 4(2|x + 3| - 2) - 1) + 3)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-5(1|((-3x - 3)/(2x + 1)) - 3| - 3)^2 - 5(1|((-3x - 3)/(2x + 1)) - 3| - 3) + 5) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-1cos(1\u03c0(1((-3x + 3)/(1x + 2)) - 4) + 1) + 2) + 3)/(2(-1cos(1\u03c0(1((-3x + 3)/(1x + 2)) - 4) + 1) + 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-4(2(-1|x| + 3)^2 + 5(-1|x| + 3) - 2)^2 - 3(2(-1|x| + 3)^2 + 5(-1|x| + 3) - 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-4(2cos(1\u03c0(-1|x - 3| + 1) - 3) - 1)) + 1| - 2 equals zero.\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) = 3|(3cos(1\u03c0(5((-2x + 1)/(1x - 2)) - 2)) - 3) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-3((1(-3sin(2\u03c0x) + 1) - 3)/(2(-3sin(2\u03c0x) + 1) + 2)) + 3) + 3)/(2(-3((1(-3sin(2\u03c0x) + 1) - 3)/(2(-3sin(2\u03c0x) + 1) + 2)) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0(1|((-3(-2|x + 2| + 2) + 3)/(-1(-2|x + 2| + 2) + 3)) - 1|) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-3|((-2((1x + 1)/(1x + 3)) + 1)/(3((1x + 1)/(1x + 3)) + 3)) - 1| + 1)) - 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": "Find the number of x-intercepts of the function f(x) = (-1(5(-3|(5x^2 + 1x) - 1| + 2) + 1) + 2)/(2(5(-3|(5x^2 + 1x) - 1| + 2) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0((2((2(1x^2 - 3x + 4) + 2)/(1(1x^2 - 3x + 4))) - 1)/(-1((2(1x^2 - 3x + 4) + 2)/(1(1x^2 - 3x + 4))) + 2))) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-3sin(3\u03c0((1(2x^2 + 5x + 2) - 1)/(3(2x^2 + 5x + 2) - 2)) + 2) + 1) - 2)/(1(-3sin(3\u03c0((1(2x^2 + 5x + 2) - 1)/(3(2x^2 + 5x + 2) - 2)) + 2) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(3cos(3\u03c0(-3|(1|x|) + 2| + 2)))^2 + 1(3cos(3\u03c0(-3|(1|x|) + 2| + 2))) - 3 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": "How many solutions does the equation (1(-2(3|(-2cos(2\u03c0x + 2) - 2) + 3| - 1) + 5) + 2)/(-2(-2(3|(-2cos(2\u03c0x + 2) - 2) + 3| - 1) + 5) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(4((-1(3sin(1\u03c0x + 2) + 3) + 2)/(3(3sin(1\u03c0x + 2) + 3) - 2))^2 - 1((-1(3sin(1\u03c0x + 2) + 3) + 2)/(3(3sin(1\u03c0x + 2) + 3) - 2))) - 2| + 2 equals zero.\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((-1(-1sin(1\u03c0(5x + 1) + 3) + 2))/(2(-1sin(1\u03c0(5x + 1) + 3) + 2) - 3)) + 3 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": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(2|(1|(-2|x + 1| - 1) - 3| + 3) - 1| + 2) - 1) - 3 equals zero.\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) = (2(1(-2|(-3cos(3\u03c0x)) - 2| - 2) + 5))/(-2(1(-2|(-3cos(3\u03c0x)) - 2| - 2) + 5) + 1) 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 2(4(2((-1x)/(-2x - 1))^2 + 1((-1x)/(-2x - 1)) - 2)^2 + 3(2((-1x)/(-2x - 1))^2 + 1((-1x)/(-2x - 1)) - 2))^2 - 3(4(2((-1x)/(-2x - 1))^2 + 1((-1x)/(-2x - 1)) - 2)^2 + 3(2((-1x)/(-2x - 1))^2 + 1((-1x)/(-2x - 1)) - 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-3|(-5(5x)) - 3| - 1) + 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((3(-2(-2cos(2\u03c0x + 3) - 1) + 1) - 1)/(1(-2(-2cos(2\u03c0x + 3) - 1) + 1) + 1)) + 2)/(-3((3(-2(-2cos(2\u03c0x + 3) - 1) + 1) - 1)/(1(-2(-2cos(2\u03c0x + 3) - 1) + 1) + 1))) equals zero.\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) = -1sin(2\u03c0(5(1(-5x^2 - 5x - 5)^2 + 4(-5x^2 - 5x - 5) + 4) - 4) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "838", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-2(-3sin(1\u03c0(3x + 5)) + 3)^2 - 5(-3sin(1\u03c0(3x + 5)) + 3) + 5) + 4 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 zeros does the function f(x) = (-3(-1sin(2\u03c0(3((2x + 2)/(1x))^2 + 4((2x + 2)/(1x)) + 1) + 1) + 1) + 1)/(-1(-1sin(2\u03c0(3((2x + 2)/(1x))^2 + 4((2x + 2)/(1x)) + 1) + 1) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-1(-3(-5x - 4)^2 + 5(-5x - 4) - 2) - 3)/(2(-3(-5x - 4)^2 + 5(-5x - 4) - 2) + 2))^2 + 1((-1(-3(-5x - 4)^2 + 5(-5x - 4) - 2) - 3)/(2(-3(-5x - 4)^2 + 5(-5x - 4) - 2) + 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0((-2((1((2x - 1)/(2x)))/(1((2x - 1)/(2x)) + 1)) + 3)/(3((1((2x - 1)/(2x)))/(1((2x - 1)/(2x)) + 1)))) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-1((1(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1))^2 - 4((1(-1|x - 1| + 3) - 3)/(2(-1|x - 1| + 3) - 1)) + 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2|(2(3sin(3\u03c0x - 2) - 2)^2 + 2(3sin(3\u03c0x - 2) - 2) - 2) - 1| - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "210", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(1(3sin(1\u03c0(-2|x| + 1) - 2) - 1)^2 - 2(3sin(1\u03c0(-2|x| + 1) - 2) - 1) - 2) - 2)/(1(1(3sin(1\u03c0(-2|x| + 1) - 2) - 1)^2 - 2(3sin(1\u03c0(-2|x| + 1) - 2) - 1) - 2)) = 0 have in the range [-10, 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) = 1(-2|((-3(1x^2 - 5) + 3)/(-1(1x^2 - 5) - 1)) - 2| + 1)^2 + 3(-2|((-3(1x^2 - 5) + 3)/(-1(1x^2 - 5) - 1)) - 2| + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(3cos(1\u03c0(-1|((1x + 3)/(2x + 2)) + 1| + 1) + 1)) + 1 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": "How many solutions does the equation 1|(-1(3(-2|x - 3| + 3)^2 - 5(-2|x - 3| + 3) + 3)^2 - 2(3(-2|x - 3| + 3)^2 - 5(-2|x - 3| + 3) + 3) + 3) + 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-3(2((2x - 2)/(2x - 1)) - 3) - 2) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "53", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(-3|(-2|x - 2|) + 1| + 1) - 1)/(-1(-3|(-2|x - 2|) + 1| + 1) - 1)) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2(3cos(1\u03c0(-5x) + 1)) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(3sin(1\u03c0((2(-5x + 5))/(-1(-5x + 5) + 3)) - 1) + 2) - 1)/(3(3sin(1\u03c0((2(-5x + 5))/(-1(-5x + 5) + 3)) - 1) + 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(2\u03c0(-4(-1|(-1x + 3) + 3| + 2)^2 - 2(-1|(-1x + 3) + 3| + 2) + 5) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "673", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2sin(1\u03c0((2((-2x + 3)/(-2x - 1)) - 1)/(1((-2x + 3)/(-2x - 1)) - 3)) - 3) - 3) + 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(5(-3sin(1\u03c0(-4x + 2) + 2)) + 2) + 1)/(1(5(-3sin(1\u03c0(-4x + 2) + 2)) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(2|(-2|((1x + 3)/(-2x - 2)) - 2| + 1) + 1| - 2)^2 + 4(2|(-2|((1x + 3)/(-2x - 2)) - 2| + 1) + 1| - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(-1((2x - 1)/(-3x))^2 + 4((2x - 1)/(-3x))) + 3)/(-1(-1((2x - 1)/(-3x))^2 + 4((2x - 1)/(-3x))) - 1)) - 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(2|(-1sin(3\u03c0((-2x)/(3x + 2)) - 1) - 3) + 1| - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3(-3sin(2\u03c0(-3|x - 3| - 3)) - 3)^2 - 2(-3sin(2\u03c0(-3|x - 3| - 3)) - 3)) - 1)/(2(-3(-3sin(2\u03c0(-3|x - 3| - 3)) - 3)^2 - 2(-3sin(2\u03c0(-3|x - 3| - 3)) - 3)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2sin(1\u03c0(-3((2x - 1)/(3x + 1)) - 1) + 3) + 2) + 2)/(-2(2sin(1\u03c0(-3((2x - 1)/(3x + 1)) - 1) + 3) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(4((-1(3x^2 + 5x + 4) - 2)/(3(3x^2 + 5x + 4) - 1)) + 1) + 1| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-1(-3sin(2\u03c0((-2x - 1)/(-1x - 3)) - 3) + 1)^2 + 5(-3sin(2\u03c0((-2x - 1)/(-1x - 3)) - 3) + 1) - 4) + 2)/(-3(-1(-3sin(2\u03c0((-2x - 1)/(-1x - 3)) - 3) + 1)^2 + 5(-3sin(2\u03c0((-2x - 1)/(-1x - 3)) - 3) + 1) - 4) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(1(-4(2x^2 - 5x + 1)^2 + 1(2x^2 - 5x + 1) + 5)^2 + 3(-4(2x^2 - 5x + 1)^2 + 1(2x^2 - 5x + 1) + 5) - 1)| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(3|(-1(2x - 3) + 2)| - 2)^2 - 2(3|(-1(2x - 3) + 2)| - 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-3(-3cos(2\u03c0(-1x + 2) + 2)) + 3)/(3(-3cos(2\u03c0(-1x + 2) + 2)) - 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-3|(-4(-2cos(2\u03c0x))) - 2| + 2) - 2 = 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 zeros does the function f(x) = -1|(2(-2((-2x + 1)/(-3x + 1)) + 3)^2 - 5(-2((-2x + 1)/(-3x + 1)) + 3) + 2) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1(2cos(3\u03c0(-2x^2 - 5x + 3) - 3) - 2))^2 - 1(-1(2cos(3\u03c0(-2x^2 - 5x + 3) - 3) - 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "991", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(-1|(4((-1x)/(3x + 3))) + 3| - 3) + 3) - 1 = 0 have in the range [-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) = (1(-2(-3(5x + 2)^2 - 5(5x + 2) + 5)^2 - 3(-3(5x + 2)^2 - 5(5x + 2) + 5) - 1) + 1)/(-2(-2(-3(5x + 2)^2 - 5(5x + 2) + 5)^2 - 3(-3(5x + 2)^2 - 5(5x + 2) + 5) - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(5(2|(-3|x - 1|) + 2| - 1) - 4)^2 - 1(5(2|(-3|x - 1|) + 2| - 1) - 4) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2|(-1(2|x - 1|)^2 + 5(2|x - 1|) - 1) - 3| - 3) - 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(5(-1|(-1x^2 + 1x) + 2| + 2) + 4)^2 + 3(5(-1|(-1x^2 + 1x) + 2| + 2) + 4) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(3cos(3\u03c0((-2(2|x + 1| - 2))/(-3(2|x + 1| - 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": "72", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2e^(-1(2((-2(-2|x + 2| + 2))/(-2(-2|x + 2| + 2) - 1))^2 + 3((-2(-2|x + 2| + 2))/(-2(-2|x + 2| + 2) - 1)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3|(-2|(1x - 3) - 1| - 1) + 3| - 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-3sin(2\u03c0((2((3x - 1)/(-3x - 2)) - 1)/(3((3x - 1)/(-3x - 2)) - 1)) + 3) - 2) + 2)/(-2(-3sin(2\u03c0((2((3x - 1)/(-3x - 2)) - 1)/(3((3x - 1)/(-3x - 2)) - 1)) + 3) - 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-5(-1((-1x - 2)/(2x + 1))^2 - 5((-1x - 2)/(2x + 1)) - 5) - 5)^2 - 2(-5(-1((-1x - 2)/(2x + 1))^2 - 5((-1x - 2)/(2x + 1)) - 5) - 5) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1(-2sin(3\u03c0((2x + 2)/(-2x + 3)) - 2) - 1)^2 - 4(-2sin(3\u03c0((2x + 2)/(-2x + 3)) - 2) - 1))^2 - 4(-1(-2sin(3\u03c0((2x + 2)/(-2x + 3)) - 2) - 1)^2 - 4(-2sin(3\u03c0((2x + 2)/(-2x + 3)) - 2) - 1)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-1(-5(5x^2 - 5x - 4) + 1) - 2)/(-2(-5(5x^2 - 5x - 4) + 1) - 1)) - 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-3(-3sin(3\u03c0(-4x + 5) - 2)) + 5)| = 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": "Determine the number of values x in [-10, 10] where f(x) = 3(-1cos(3\u03c0((2(-1x - 2))/(-2(-1x - 2) - 3)) + 3) - 2) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "76", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-1(2(-1|x| + 3)^2 + 3(-1|x| + 3) - 2) - 5) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0((2(-3|((3x - 3)/(-2x - 2)) - 3| + 3) + 2)/(-2(-3|((3x - 3)/(-2x - 2)) - 3| + 3) + 3)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2cos(3\u03c0(2|(-1|x + 2| + 2) + 1| - 1) + 2) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1|(-1(-5x + 2) + 1) + 2| - 2) - 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0(1|(2((-3x + 2)/(-1x + 2)) + 5) - 1| - 2) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "168", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(-1(-1|((2(-2x^2 + 5x + 5) - 3)/(-1(-2x^2 + 5x + 5) + 2)) + 2| + 3)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(-1|(3((-2x - 1)/(3x - 1)) + 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": "81", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((1((-1(-1x^2 - 4x - 1) - 2)/(1(-1x^2 - 4x - 1) + 3)))/(-1((-1(-1x^2 - 4x - 1) - 2)/(1(-1x^2 - 4x - 1) + 3)) + 2)) - 1) = 0 have in the range [-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 -3|((1(-3cos(1\u03c0(-1x - 1) - 1)) - 1)/(2(-3cos(1\u03c0(-1x - 1) - 1)) + 2))| + 2 = 0 have in the range [-10, 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 3|(3cos(2\u03c0(-1(5x - 3) - 1) + 2) + 1) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-5(-3sin(1\u03c0(4x + 4) - 1) - 3) - 5) + 2)/(-2(-5(-3sin(1\u03c0(4x + 4) - 1) - 3) - 5) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3cos(3\u03c0(-5(-2|x + 2| - 1)) - 3) - 1)^2 + 1(3cos(3\u03c0(-5(-2|x + 2| - 1)) - 3) - 1) - 2 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) = 2(1(2|(4x - 3) - 2|) - 4)^2 - 2(1(2|(4x - 3) - 2|) - 4) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1cos(2\u03c0(-5(4x + 3)^2 + 5(4x + 3) - 2) + 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1228", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-3sin(3\u03c0(1(-1|x| + 3) - 1) - 2) + 2))/(-1(-3sin(3\u03c0(1(-1|x| + 3) - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(2cos(2\u03c0(4(-1x^2 + 2x - 1)^2 - 1(-1x^2 + 2x - 1)) + 2) + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1128", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-5(-2cos(3\u03c0((-2x - 3)/(-3x + 1)) + 3) - 2)^2 + 2(-2cos(3\u03c0((-2x - 3)/(-3x + 1)) + 3) - 2) + 5) - 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3(-5(-1x + 3) + 2)^2 - 1(-5(-1x + 3) + 2) - 1)^2 - 1(3(-5(-1x + 3) + 2)^2 - 1(-5(-1x + 3) + 2) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0((-3((3((-2x - 2)/(2x + 3)) - 2)/(2((-2x - 2)/(2x + 3)) + 2)) - 3)/(-2((3((-2x - 2)/(2x + 3)) - 2)/(2((-2x - 2)/(2x + 3)) + 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": "11", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-3((-3(2|x - 3| - 3))/(-3(2|x - 3| - 3) + 2))^2 - 5((-3(2|x - 3| - 3))/(-3(2|x - 3| - 3) + 2)) - 2) - 1)/(2(-3((-3(2|x - 3| - 3))/(-3(2|x - 3| - 3) + 2))^2 - 5((-3(2|x - 3| - 3))/(-3(2|x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((3(-1cos(2\u03c0(-1x + 4)) + 1))/(2(-1cos(2\u03c0(-1x + 4)) + 1) - 1)) - 5 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) = -2|(2|((-2(-3x^2 + 2x + 3) + 3)/(1(-3x^2 + 2x + 3) - 2)) - 1| - 3) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(-2|(1(3x^2 - 3x + 2)^2 - 1(3x^2 - 3x + 2) + 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": "815", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(3(2sin(1\u03c0((-2x + 3)/(1x + 1)) - 1))^2 + 1(2sin(1\u03c0((-2x + 3)/(1x + 1)) - 1)) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(3\u03c0((3(2|(-4x^2 + 2x + 1) + 3| + 3) + 3)/(2(2|(-4x^2 + 2x + 1) + 3| + 3))) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(2|(-5(-3cos(3\u03c0x - 3) + 2)^2 + 4(-3cos(3\u03c0x - 3) + 2) + 5) + 2| - 1) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "183", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-5(-2cos(2\u03c0((2x - 3)/(-2x - 3)) - 1) - 2) - 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|((1(2(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) + 1))/(-1(2(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) + 1) - 1)) + 2| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0((2(1(-3x + 3) - 1) - 2)/(-3(1(-3x + 3) - 1) - 1)) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-3(-1|(2|x| - 3)| - 1) - 5) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((2(5(2|x + 2|)^2 + 4(2|x + 2|) - 5) - 3)/(1(5(2|x + 2|)^2 + 4(2|x + 2|) - 5) + 2)) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-1(3(2x^2 - 4x + 1) + 2))/(1(3(2x^2 - 4x + 1) + 2) - 2))^2 + 5((-1(3(2x^2 - 4x + 1) + 2))/(1(3(2x^2 - 4x + 1) + 2) - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-5(1sin(1\u03c0(-1x^2 + 2x - 5) + 2)) + 4))/(1(-5(1sin(1\u03c0(-1x^2 + 2x - 5) + 2)) + 4) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "202", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0((-1(1(5x - 1) + 1) + 3)/(-3(1(5x - 1) + 1))) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2e^(-1(-2(5(3x^2 + 5x - 3) - 3)^2 + 5(5(3x^2 + 5x - 3) - 3) - 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|((-2(4(-2cos(1\u03c0x + 2) - 1)^2 + 5(-2cos(1\u03c0x + 2) - 1) + 2) - 3)/(-2(4(-2cos(1\u03c0x + 2) - 1)^2 + 5(-2cos(1\u03c0x + 2) - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(2(-3|(2cos(2\u03c0x) + 3) - 1| - 2)^2 + 3(-3|(2cos(2\u03c0x) + 3) - 1| - 2) - 4) + 5 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": "How many zeros does the function f(x) = 3sin(2\u03c0(2(-4(-2x - 1) + 3) - 4) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2e^(-2(3|(3x^2 - 5x - 2) + 1| - 1)) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(1|(1(-3cos(2\u03c0x + 2) - 1) - 3) + 2| + 1)^2 + 2(1|(1(-3cos(2\u03c0x + 2) - 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": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((2(-3sin(3\u03c0(-2x^2 + 2x + 1) - 2) - 1) + 1)/(3(-3sin(3\u03c0(-2x^2 + 2x + 1) - 2) - 1) + 3)) - 3)/(1((2(-3sin(3\u03c0(-2x^2 + 2x + 1) - 2) - 1) + 1)/(3(-3sin(3\u03c0(-2x^2 + 2x + 1) - 2) - 1) + 3))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "187", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(3(-4(-3x^2 - 5x + 4)^2 + 3(-3x^2 - 5x + 4) - 3) + 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1246", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(4(3|(3x - 1) + 1| - 3)^2 - 3(3|(3x - 1) + 1| - 3) - 5) + 2)/(-1(4(3|(3x - 1) + 1| - 3)^2 - 3(3|(3x - 1) + 1| - 3) - 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(1|(-3cos(2\u03c0(-2|x - 1| + 2)) - 1) + 3| - 2)^2 - 4(1|(-3cos(2\u03c0(-2|x - 1| + 2)) - 1) + 3| - 2) - 1 = 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": "Determine the number of values x in [-10, 10] where f(x) = 2(1|(1|(-3|x| + 2) + 1| - 1)| + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(2(1(-1sin(1\u03c0x - 3) + 2)^2 - 3) + 2) - 4 = 0 have in the range [-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) = -4(-2(3(2sin(3\u03c0x - 2) + 1)^2 - 2(2sin(3\u03c0x - 2) + 1) - 2) + 5)^2 - 1(-2(3(2sin(3\u03c0x - 2) + 1)^2 - 2(2sin(3\u03c0x - 2) + 1) - 2) + 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2((2(5(1cos(3\u03c0x - 2) + 1) - 3) - 3)/(3(5(1cos(3\u03c0x - 2) + 1) - 3))) - 1)/(-2((2(5(1cos(3\u03c0x - 2) + 1) - 3) - 3)/(3(5(1cos(3\u03c0x - 2) + 1) - 3))) - 1) equals zero.\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(-2|(1(4x^2 + 2x + 1)^2 - 4(4x^2 + 2x + 1) + 1) + 1| - 2) + 3)/(3(-2|(1(4x^2 + 2x + 1)^2 - 4(4x^2 + 2x + 1) + 1) + 1| - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(3\u03c0(-2|(-1(-4x^2 + 2x + 2) - 1) - 1| - 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1074", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0(1|(-4((2x + 1)/(1x - 2))^2 - 5((2x + 1)/(1x - 2)) - 5) + 1| + 1) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2e^(2(-5(5(3|x + 1| - 3)^2 + 4(3|x + 1| - 3) + 1)^2 - 5(5(3|x + 1| - 3)^2 + 4(3|x + 1| - 3) + 1) + 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2cos(2\u03c0(-2((-2x + 2)/(-3x + 2))^2 + 5((-2x + 2)/(-3x + 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": "38", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(3|(4(2|x - 3| - 2) + 3) - 2| - 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(-4(4(-1x^2 - 1x) - 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": "1227", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(1|((3(3|x + 1| - 2) + 1)/(3(3|x + 1| - 2) - 2)) + 3| - 3) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-4(1(2x - 5)^2 + 5(2x - 5) + 4) - 4) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-3(-2(1cos(3\u03c0x + 2) + 3)^2 + 3(1cos(3\u03c0x + 2) + 3) + 4)^2 + 5) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1|(3sin(1\u03c0(-1x^2 + 1x - 5) + 3) - 2) - 2| - 1)^2 + 5(1|(3sin(1\u03c0(-1x^2 + 1x - 5) + 3) - 2) - 2| - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0((1(-5(-1|x - 1|)) + 2)/(-2(-5(-1|x - 1|)) + 3))) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-3sin(1\u03c0(1(-1x - 2) - 4) + 3) + 1)^2 + 2(-3sin(1\u03c0(1(-1x - 2) - 4) + 3) + 1) - 5 = 0 have in the range [-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) = 2(-3sin(3\u03c0(-2(-3x^2 + 1x - 5)^2 + 3(-3x^2 + 1x - 5) + 1) - 1) + 2)^2 + 5(-3sin(3\u03c0(-2(-3x^2 + 1x - 5)^2 + 3(-3x^2 + 1x - 5) + 1) - 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "492", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-4(-3sin(2\u03c0(-2|x + 2| + 3) + 3) - 2) - 5) + 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": "Determine the number of values x in [-10, 10] where f(x) = -1|(2sin(1\u03c0(-1|(-3|x - 2| - 1)| - 1) + 2) + 1) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(1(-2|(1|x + 2| + 1) + 2| + 3)^2 + 4(-2|(1|x + 2| + 1) + 2| + 3) + 1)^2 + 4(1(-2|(1|x + 2| + 1) + 2| + 3)^2 + 4(-2|(1|x + 2| + 1) + 2| + 3) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-1cos(3\u03c0(5((2x + 3)/(-2x + 3)) + 2)) + 1) + 3)/(-3(-1cos(3\u03c0(5((2x + 3)/(-2x + 3)) + 2)) + 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "227", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3(-2cos(1\u03c0((-1x + 1)/(2x)) - 3)) + 1)^2 - 1(-3(-2cos(1\u03c0((-1x + 1)/(2x)) - 3)) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(2(1(-3|x - 2|)^2 + 5(-3|x - 2|) + 3)^2 - 3(1(-3|x - 2|)^2 + 5(-3|x - 2|) + 3) + 4) - 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(3|(-1|(3|x + 3| + 3)| - 2) + 3| + 1) + 1) + 1 equals zero.\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) = (1(2(3|(2cos(1\u03c0x + 2) + 3) - 3| - 1) - 5) + 3)/(3(2(3|(2cos(1\u03c0x + 2) + 3) - 3| - 1) - 5) + 3) 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) = -2cos(1\u03c0(-2((3((1x - 3)/(1x + 2)) + 3)/(-1((1x - 3)/(1x + 2)) + 3))^2 + 2((3((1x - 3)/(1x + 2)) + 3)/(-1((1x - 3)/(1x + 2)) + 3)) - 2) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1cos(3\u03c0(-3|((-3x - 3)/(2x - 1)) - 2|) - 2) - 1) - 3)/(2(1cos(3\u03c0(-3|((-3x - 3)/(2x - 1)) - 2|) - 2) - 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(1sin(2\u03c0(-1((1x - 1)/(1x - 3)) + 1) - 1) - 1) - 2)/(2(1sin(2\u03c0(-1((1x - 1)/(1x - 3)) + 1) - 1) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "74", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0((2(-2|((-2x - 1)/(-1x - 1)) - 1| - 1) - 2)/(3(-2|((-2x - 1)/(-1x - 1)) - 1| - 1) + 2))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(4(-2sin(2\u03c0(3|x + 2| + 3) - 3) - 1)^2 - 1(-2sin(2\u03c0(3|x + 2| + 3) - 3) - 1) - 2))/(2(4(-2sin(2\u03c0(3|x + 2| + 3) - 3) - 1)^2 - 1(-2sin(2\u03c0(3|x + 2| + 3) - 3) - 1) - 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|(-3|(3cos(2\u03c0x - 2) + 3) - 2| - 1) + 2| + 2)^2 - 3(-1|(-3|(3cos(2\u03c0x - 2) + 3) - 2| - 1) + 2| + 2) + 1 equals zero.\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 2sin(1\u03c0(4((3((-2x + 2)/(-2x + 3)) + 3)/(2((-2x + 2)/(-2x + 3)) + 1)) - 4) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(-1(-3|((-1x - 1)/(-3x - 1)) - 2| + 1) - 4) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1(-4(-1|x| + 2)^2 + 1(-1|x| + 2) + 1)^2 - 5(-4(-1|x| + 2)^2 + 1(-1|x| + 2) + 1) - 3) - 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-1|(-3(-2cos(3\u03c0x + 2) - 3)^2 - 5(-2cos(3\u03c0x + 2) - 3) - 3) + 1| + 3) - 5 = 0 have in the range [-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) = -2cos(3\u03c0(-1|(-4(-2x + 2)^2 - 5(-2x + 2) - 1) - 1| - 3) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1131", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(-2(2cos(2\u03c0x + 3)) - 3)^2 + 5(-2(2cos(2\u03c0x + 3)) - 3) - 1) equals zero.\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) = 2|(-1cos(2\u03c0(-3|(-1|x + 2| - 2) - 2| + 1)) + 3) - 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(3\u03c0(-2|(-3(1x^2 - 4x - 2) + 1) - 2| + 2) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1100", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(-1|(1sin(3\u03c0((-2x - 2)/(2x - 1)) + 1) + 3) - 3| + 2) - 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(1((2(-2cos(1\u03c0x - 3) - 2) + 3)/(-3(-2cos(1\u03c0x - 3) - 2) - 3)) + 5) - 1 = 0 have in the range [-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(-2(1(-4x^2 - 1x + 5)^2 - 5(-4x^2 - 1x + 5) + 2) + 2) - 3)/(-1(-2(1(-4x^2 - 1x + 5)^2 - 5(-4x^2 - 1x + 5) + 2) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3cos(1\u03c0(-5((1x + 1)/(2x + 1))^2 + 3((1x + 1)/(2x + 1)) + 2) - 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "39", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(1\u03c0(-4((3((-2x - 1)/(-2x + 3)) + 1)/(2((-2x - 1)/(-2x + 3)) + 3))^2 - 3((3((-2x - 1)/(-2x + 3)) + 1)/(2((-2x - 1)/(-2x + 3)) + 3))) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1(2(-1cos(2\u03c0x) + 2) - 3) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((2(-5(2|x + 3| - 1) + 3) + 3)/(-2(-5(2|x + 3| - 1) + 3) - 2)) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-1|(-4((3x - 2)/(-1x))^2 + 1((3x - 2)/(-1x))) - 2| + 3)^2 + 1(-1|(-4((3x - 2)/(-1x))^2 + 1((3x - 2)/(-1x))) - 2| + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((3(2sin(2\u03c0(-1x^2 + 3x - 5) + 1)) - 1)/(2(2sin(2\u03c0(-1x^2 + 3x - 5) + 1)) - 3))^2 + 1((3(2sin(2\u03c0(-1x^2 + 3x - 5) + 1)) - 1)/(2(2sin(2\u03c0(-1x^2 + 3x - 5) + 1)) - 3)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "403", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-2|(4(-2x^2 + 3x)) + 1| + 3) - 3)/(-1(-2|(4(-2x^2 + 3x)) + 1| + 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-4((-3(-2sin(2\u03c0x + 3) - 1))/(-3(-2sin(2\u03c0x + 3) - 1) - 2)) - 5) - 3)/(-1(-4((-3(-2sin(2\u03c0x + 3) - 1))/(-3(-2sin(2\u03c0x + 3) - 1) - 2)) - 5)) equals zero.\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) = -4(2((1(-3|x + 1|) - 3)/(2(-3|x + 1|) - 1)) - 5)^2 - 3(2((1(-3|x + 1|) - 3)/(2(-3|x + 1|) - 1)) - 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0(3|(-5(2|x - 2| - 1)^2 + 4(2|x - 2| - 1) + 1) + 2| + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1161", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(-1|(2|(3|x - 3| + 1) + 3| + 1)| + 2) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(3sin(2\u03c0(4(-3|x - 1| - 1) - 5) - 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(1\u03c0(-1|(-2|(-4x^2 - 2x) - 1| + 2)| + 3) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "677", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0((2(2(-4x + 1)^2 - 4(-4x + 1) + 1))/(-2(2(-4x + 1)^2 - 4(-4x + 1) + 1) + 3)) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-3(-3sin(3\u03c0((-3x - 3)/(1x - 2)) - 2) + 3)^2 - 5(-3sin(3\u03c0((-3x - 3)/(1x - 2)) - 2) + 3) + 4) + 1| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(1((-1(5x^2 - 2x - 2) - 1)/(-3(5x^2 - 2x - 2) - 2)))^2 - 5(1((-1(5x^2 - 2x - 2) - 1)/(-3(5x^2 - 2x - 2) - 2))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(1(-1(-1x + 3) - 4)^2 - 1(-1(-1x + 3) - 4) + 5) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "285", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(4(-3sin(2\u03c0(-4x^2 - 5x + 5) - 2) - 3) + 3)^2 + 2(4(-3sin(2\u03c0(-4x^2 - 5x + 5) - 2) - 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "224", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-5(-1((1x - 1)/(1x - 3))^2 + 3((1x - 1)/(1x - 3)) - 1)^2 - 1(-1((1x - 1)/(1x - 3))^2 + 3((1x - 1)/(1x - 3)) - 1) + 5) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0(2|(-2|(3x^2 + 4x - 4) + 3| + 3) + 1| - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "943", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(-2cos(2\u03c0(2|(-3|x + 3| - 2) + 3| - 1) + 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-2|(5(5x^2 - 1x - 2)^2 + 5(5x^2 - 1x - 2) + 2) - 3|) - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "500", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(2\u03c0(4((-3(4x - 1) - 3)/(-1(4x - 1) + 2)) + 1) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(-5(-3((3x + 2)/(-1x - 2)) + 4) - 1) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "458", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(2cos(2\u03c0((-3((1x - 2)/(-1x + 3)) + 2)/(1((1x - 2)/(-1x + 3)) + 1))))^2 + 2(2cos(2\u03c0((-3((1x - 2)/(-1x + 3)) + 2)/(1((1x - 2)/(-1x + 3)) + 1)))) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(5(-2|(3x^2 + 4x) - 2| + 3)) - 1)/(1(5(-2|(3x^2 + 4x) - 2| + 3))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(1(2|(1x + 4) + 3| - 3)^2 - 5(2|(1x + 4) + 3| - 3) + 3)^2 - 5(1(2|(1x + 4) + 3| - 3)^2 - 5(2|(1x + 4) + 3| - 3) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-5(2e^(2(1|x + 2| - 1)) - 2)^2 + 4(2e^(2(1|x + 2| - 1)) - 2) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-2(-3|(1x) - 1| + 1)^2 - 2(-3|(1x) - 1| + 1) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1((-2(-5(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) + 5) + 2)/(3(-5(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) + 5))) + 1)/(-3((-2(-5(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) + 5) + 2)/(3(-5(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) + 5))) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-2(-1(1x^2 - 1x - 3)^2 + 2(1x^2 - 1x - 3))^2 - 4(-1(1x^2 - 1x - 3)^2 + 2(1x^2 - 1x - 3)) + 2)^2 + 4(-2(-1(1x^2 - 1x - 3)^2 + 2(1x^2 - 1x - 3))^2 - 4(-1(1x^2 - 1x - 3)^2 + 2(1x^2 - 1x - 3)) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((2(4(3cos(3\u03c0x - 2) - 3)^2 - 1(3cos(3\u03c0x - 2) - 3) - 5) + 2)/(-1(4(3cos(3\u03c0x - 2) - 3)^2 - 1(3cos(3\u03c0x - 2) - 3) - 5) + 3)) - 2)/(2((2(4(3cos(3\u03c0x - 2) - 3)^2 - 1(3cos(3\u03c0x - 2) - 3) - 5) + 2)/(-1(4(3cos(3\u03c0x - 2) - 3)^2 - 1(3cos(3\u03c0x - 2) - 3) - 5) + 3)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1|(2cos(2\u03c0((1x - 3)/(-1x - 1)) - 3) + 1) - 3| + 3) - 2)/(-3(-1|(2cos(2\u03c0((1x - 3)/(-1x - 1)) - 3) + 1) - 3| + 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-5(-1(3sin(1\u03c0x + 1) + 1) + 2)^2 - 1(-1(3sin(1\u03c0x + 1) + 1) + 2) + 4) + 5 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) = 3sin(3\u03c0(-4(3|((3x - 2)/(2x - 3)) - 2| + 1)) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "230", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-3sin(2\u03c0(1|((-2x + 3)/(-1x - 3)) + 3| - 1) - 2) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|(-2(-1x + 2)^2 + 5(-1x + 2) - 2) + 3|)^2 + 3(-3|(-2(-1x + 2)^2 + 5(-1x + 2) - 2) + 3|) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(3cos(1\u03c0(1|((1x - 1)/(2x - 1)) - 2| + 3) + 2) + 2) - 1 where -10 \u2264 x \u2264 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) = 2sin(2\u03c0(3|(4(-2|x + 1| - 3) + 1) - 2| - 2) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(3cos(2\u03c0(4((-1x - 3)/(3x - 2)) + 3) - 2) - 2)| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-3(-1(2x^2 - 5x - 4)^2 - 1(2x^2 - 5x - 4) + 5)^2 - 1(-1(2x^2 - 5x - 4)^2 - 1(2x^2 - 5x - 4) + 5) - 1) - 3)/(-3(-3(-1(2x^2 - 5x - 4)^2 - 1(2x^2 - 5x - 4) + 5)^2 - 1(-1(2x^2 - 5x - 4)^2 - 1(2x^2 - 5x - 4) + 5) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(1(4((1x + 3)/(-3x - 3)) - 3) - 3) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1((2(-3cos(3\u03c0x + 3) + 2) + 3)/(1(-3cos(3\u03c0x + 3) + 2) - 2))) + 3 = 0 have in the range [-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) = 2e^(-1(3|(-4((-3x)/(-1x + 2))^2 - 5((-3x)/(-1x + 2)) + 4)| + 1)) where -10 \u2264 x \u2264 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) = (-2(-4(-1cos(1\u03c0((2x - 3)/(-2x - 3)) + 3) - 1)^2 - 5(-1cos(1\u03c0((2x - 3)/(-2x - 3)) + 3) - 1) + 4) - 1)/(-1(-4(-1cos(1\u03c0((2x - 3)/(-2x - 3)) + 3) - 1)^2 - 5(-1cos(1\u03c0((2x - 3)/(-2x - 3)) + 3) - 1) + 4) - 2) 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|(1(2(-5x - 2)^2 - 1(-5x - 2) - 1) - 4) - 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(3\u03c0(4((3(1x^2 - 4) - 1)/(-2(1x^2 - 4) - 1)) + 5) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "144", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((3(-3sin(1\u03c0((-1x + 3)/(3x + 1)) - 3) + 3) - 1)/(2(-3sin(1\u03c0((-1x + 3)/(3x + 1)) - 3) + 3) - 1)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(1cos(1\u03c0(2(1|x + 3| + 3)^2 - 4) + 2) - 3) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "676", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2|(-2((-1x - 1)/(-1x + 2)) + 3) + 3| - 2)^2 + 5(2|(-2((-1x - 1)/(-1x + 2)) + 3) + 3| - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(4(-5(-5x + 4)^2 + 2(-5x + 4) - 3) - 1) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1199", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1(2|(-3|x + 2| + 1)| - 1) + 2)^2 - 5(-1(2|(-3|x + 2| + 1)| - 1) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}