{"messages": [{"content": "How many zeros does the function f(x) = -1((1(2|(3x)| + 2) - 1)/(-1(2|(3x)| + 2) + 2))^2 + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-3sin(3\u03c0x - 3) + 1) + 2)/(-2(-3sin(3\u03c0x - 3) + 1) - 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": "Determine the number of values x in [-10, 10] where f(x) = 1(1((-2(-1|x + 1| - 2) - 1)/(1(-1|x + 1| - 2) + 3)) + 5)^2 + 2(1((-2(-1|x + 1| - 2) - 1)/(1(-1|x + 1| - 2) + 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 5(2cos(2\u03c0(3|(4x^2 + 1x - 3) - 3| - 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": "799", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-1(-1|(-1x + 5) + 2| - 1)^2 - 1(-1|(-1x + 5) + 2| - 1) + 2) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "636", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2((2x)/(1x + 1))^2 - 4((2x)/(1x + 1)) - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1e^(2(-3((-1(-4x^2 + 3x + 2))/(3(-4x^2 + 3x + 2) + 3)) - 2)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0((2(-3|x - 2| - 2) - 3)/(-1(-3|x - 2| - 2) + 3))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|((2(-2(-2x^2 - 1x - 5) - 2) - 2)/(1(-2(-2x^2 - 1x - 5) - 2) + 3)) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2|(1((-1x - 3)/(3x - 2))^2 - 4((-1x - 3)/(3x - 2)) - 3) - 1| - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0(-2|((2(-5x^2 + 5) - 3)/(-1(-5x^2 + 5) + 2)) - 1| + 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = (2(3(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 1)) + 1)/(1(3(-1|x - 1| + 1)^2 + 3(-1|x - 1| + 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(-3sin(1\u03c0x + 1) - 3) equals zero.\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) = (-3(3cos(1\u03c0(-4x^2 + 2x - 3) + 1) - 3) - 2)/(2(3cos(1\u03c0(-4x^2 + 2x - 3) + 1) - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "497", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(3|x + 3|) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-2|(3x^2 - 1x - 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": "How many solutions does the equation (-3(2cos(3\u03c0(-3|(1x^2 - 3x - 2) - 2|) - 3) + 1) - 1)/(-1(2cos(3\u03c0(-3|(1x^2 - 3x - 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": "1177", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3|(2cos(1\u03c0x + 1) - 3) + 3| + 3) - 1)/(1(-3|(2cos(1\u03c0x + 1) - 3) + 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|(1(-2((3x - 3)/(-2x + 3))^2 + 4((3x - 3)/(-2x + 3)) + 3) - 2) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(1|(1((3x + 1)/(1x + 1)) + 1) - 1| + 1)^2 - 2(1|(1((3x + 1)/(1x + 1)) + 1) - 1| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(2\u03c0(-1x - 2)) + 1 = 0 have in the range [-10, 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) = (-1(2(2(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2)) - 5))/(-2(2(2(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 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": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0(-3|(4x^2 + 2x - 1) + 2| - 2) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2sin(1\u03c0(1|x| - 1) - 2) + 1)^2 - 2(-2sin(1\u03c0(1|x| - 1) - 2) + 1) + 1 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) = 5(-3((-2x - 3)/(1x + 3))^2 + 1((-2x - 3)/(1x + 3)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(1|(-2x + 1) + 3|)^2 + 4(1|(-2x + 1) + 3|) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-4((3(1e^(2x) - 1) - 2)/(-3(1e^(2x) - 1) + 4)))^2 + 3(-4((3(1e^(2x) - 1) - 2)/(-3(1e^(2x) - 1) + 4))) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0(-2x^2 - 2x - 4) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1168", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(3(-1|((2x + 2)/(-3x - 2)) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-1|(-1e^(-1x) + 2) + 3| + 2)^2 + 3(-1|(-1e^(-1x) + 2) + 3| + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(2(5(-1|x| + 3)^2 + 5(-1|x| + 3)) - 1) + 1)/(1(2(5(-1|x| + 3)^2 + 5(-1|x| + 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 5(-2|((2(-4x - 3) + 2)/(-2(-4x - 3) - 1)) - 2| - 1)^2 + 5(-2|((2(-4x - 3) + 2)/(-2(-4x - 3) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(-4x^2 - 1x - 2) + 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1338", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|((-2(-2(-3sin(3\u03c0x + 3) - 1)^2 + 5(-3sin(3\u03c0x + 3) - 1) - 1) + 2)/(2(-2(-3sin(3\u03c0x + 3) - 1)^2 + 5(-3sin(3\u03c0x + 3) - 1) - 1) + 2)) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "146", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((-1(-3|(1x + 3) - 1| + 3) - 2)/(2(-3|(1x + 3) - 1| + 3) + 2))^2 - 1((-1(-3|(1x + 3) - 1| + 3) - 2)/(2(-3|(1x + 3) - 1| + 3) + 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": "How many zeros does the function f(x) = -3cos(2\u03c0(3|(-3x^2 - 3x + 4) - 2| - 2) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1613", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(-5x^2 + 2x - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1000", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-3sin(3\u03c0x) + 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": "How many zeros does the function f(x) = 2(-3(-2|x - 1|)^2 + 2(-2|x - 1|) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-1|(5(-2x^2 + 1x + 3) + 4) - 1| + 2) - 2)/(-2(-1|(5(-2x^2 + 1x + 3) + 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) = (3(1cos(1\u03c0(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) + 1) + 3)))/(-1(1cos(1\u03c0(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) + 1) + 3)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1412", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3cos(3\u03c0(5(2|x| - 3)^2 + 2(2|x| - 3) - 5) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1041", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-3sin(2\u03c0x + 3))^2 - 2(-3sin(2\u03c0x + 3)) - 3 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) = (2(1(-2cos(3\u03c0x - 1) + 2) - 2) + 3)/(3(1(-2cos(3\u03c0x - 1) + 2) - 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(2|(3x^2 - 3x + 2) - 1| - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-3x^2 + 3x + 3) + 2)/(2(-3x^2 + 3x + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3((3(-1x + 2) + 1)/(2(-1x + 2)))^2 + 4((3(-1x + 2) + 1)/(2(-1x + 2))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3((-1x + 1)/(3x))^2 - 5((-1x + 1)/(3x)) + 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((-1(2(2|x - 3| - 1) + 3) + 3)/(1(2(2|x - 3| - 1) + 3) - 2))^2 - 5((-1(2(2|x - 3| - 1) + 3) + 3)/(1(2(2|x - 3| - 1) + 3) - 2)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-2e^(-2(1(2x^2 + 4x - 2) - 5)) + 2) + 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": "Determine the number of values x in [-10, 10] where f(x) = -1((-2(1(1|x| - 2)^2 - 3(1|x| - 2) - 2) + 3)/(-1(1(1|x| - 2)^2 - 3(1|x| - 2) - 2))) - 5 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((1(-5x^2 - 5x - 2) + 1)/(1(-5x^2 - 5x - 2) - 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": "Find the number of x-intercepts of the function f(x) = -3(-1|x| + 1)^2 + 3(-1|x| + 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0((-2x - 2)/(-1x + 2)) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-1x^2 - 5x + 5) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2((-3x - 1)/(1x)) - 1) + 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(3cos(1\u03c0(-1|x + 2| - 3) - 1) + 1))/(-2(3cos(1\u03c0(-1|x + 2| - 3) - 1) + 1) - 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": "How many zeros does the function f(x) = 2cos(1\u03c0(1((-2(-4x^2 - 5x - 4))/(-1(-4x^2 - 5x - 4) - 3)) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(2\u03c0((2(-3x - 4) - 2)/(-1(-3x - 4) - 3)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "88", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-1cos(3\u03c0(3x - 3) + 2) + 3) - 2)/(1(-1cos(3\u03c0(3x - 3) + 2) + 3)) = 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": "Determine the number of values x in [-10, 10] where f(x) = -1cos(1\u03c0(1|x - 1| - 1) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((2(-1(-1x + 4)^2 - 5(-1x + 4) + 4) + 3)/(-3(-1(-1x + 4)^2 - 5(-1x + 4) + 4) + 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) = 4(3|(4x^2 - 1x - 5) + 3| - 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 zeros does the function f(x) = -3|(-1cos(2\u03c0x - 2) - 3) + 1| + 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) = -4(2|(-1x^2 - 2x + 3) + 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 zeros does the function f(x) = (-3(3(-1x - 5)^2 + 5(-1x - 5) + 2) + 1)/(2(3(-1x - 5)^2 + 5(-1x - 5) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(4(1sin(3\u03c0x + 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(2((-3x + 2)/(3x + 1))^2 + 4((-3x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(-3|((-2x - 1)/(-3x + 4)) - 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": "118", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|((-3(2(-5x - 1)^2 - 5))/(3(2(-5x - 1)^2 - 5) - 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 solutions does the equation (-1(3(3cos(3\u03c0x + 3) + 1)^2 + 4(3cos(3\u03c0x + 3) + 1) + 3) + 3)/(-1(3(3cos(3\u03c0x + 3) + 1)^2 + 4(3cos(3\u03c0x + 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": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((-2(-4(1x^2 + 4x) + 2) + 2)/(-2(-4(1x^2 + 4x) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-2|(5((-2x - 2)/(-1x - 2))^2 + 5((-2x - 2)/(-1x - 2)) - 5) - 1| + 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": "How many zeros does the function f(x) = 1|((-1(4(-1x^2 + 5x + 2) - 1) - 2)/(-3(4(-1x^2 + 5x + 2) - 1) + 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": "How many solutions does the equation (-2(-2(-1|x + 2| + 3)^2 + 2) - 2)/(-2(-2(-1|x + 2| + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1x - 1)^2 - 4(1x - 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|((-2(-5x - 3) + 2)/(-3(-5x - 3) + 4)) - 1| - 3)^2 - 2(2|((-2(-5x - 3) + 2)/(-3(-5x - 3) + 4)) - 1| - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(1\u03c0(-4x^2 + 5) + 1) - 1 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 zeros does the function f(x) = 1e^(2((-2(-4(-1x - 5)^2 + 1(-1x - 5) + 2) + 1)/(3(-4(-1x - 5)^2 + 1(-1x - 5) + 2) - 1))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(2\u03c0(-2(3(1|x - 3| + 2) + 5)^2 - 1(3(1|x - 3| + 2) + 5) + 5)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1182", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(5x + 4)^2 + 5(5x + 4) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-4(-3sin(3\u03c0x) + 2) + 3))/(-1(-4(-3sin(3\u03c0x) + 2) + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((3(4(1|x - 3| - 3)^2 - 2) - 2)/(1(4(1|x - 3| - 3)^2 - 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": "Determine the number of values x in [-10, 10] where f(x) = -1|(-1x - 4) - 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-1sin(1\u03c0x + 2) - 1) - 1)/(-2(-1sin(1\u03c0x + 2) - 1) + 3) = 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": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1|(5x^2 - 4x + 2) - 3| + 3) - 2)/(1(-1|(5x^2 - 4x + 2) - 3| + 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(5(-3sin(2\u03c0(2|x - 3| + 1) - 1) + 1)^2 + 5(-3sin(2\u03c0(2|x - 3| + 1) - 1) + 1) - 2) - 5 = 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) = -3((-2(2|x + 3| - 2) + 2)/(2(2|x + 3| - 2) + 3)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-3cos(2\u03c0(-3|x| - 3) - 1) + 2) - 3)/(2(-3cos(2\u03c0(-3|x| - 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": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3((2(5x^2 + 5x + 2) - 3)/(2(5x^2 + 5x + 2) + 2))) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(4x - 3)^2 - 1(4x - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(1((3x - 2)/(2x - 3))^2 - 1((3x - 2)/(2x - 3)) - 4) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3(-1(-1|x + 2| + 2)^2 - 3(-1|x + 2| + 2) + 5)) - 2)/(2(-3(-1(-1|x + 2| + 2)^2 - 3(-1|x + 2| + 2) + 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": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0((-1x - 2)/(-2x + 3)) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(2(5(-2|x| + 1)^2 + 5(-2|x| + 1) - 2) - 5) + 1)/(-3(2(5(-2|x| + 1)^2 + 5(-2|x| + 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": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(-3x - 4) + 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": "Determine the number of values x in [-10, 10] where f(x) = -1(3|(-2cos(1\u03c0x - 1) + 1) - 2|)^2 + 1(3|(-2cos(1\u03c0x - 1) + 1) - 2|) + 4 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) = -1cos(2\u03c0(1|x - 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": "Determine the number of values x in [-10, 10] where f(x) = -3(5((1x - 2)/(-2x + 1)) - 5)^2 - 3(5((1x - 2)/(-2x + 1)) - 5) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(1(-3x)^2 - 2(-3x) - 3) - 2) - 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": "Find the number of x-intercepts of the function f(x) = 4(5(-2|((2x - 2)/(3x + 3))| + 2)^2 + 3(-2|((2x - 2)/(3x + 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 5(1|x + 3| - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(2(1|(-5x - 3) + 2| + 2)^2 - 4(1|(-5x - 3) + 2| + 2) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1580", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(1|((1x - 2)/(-3x)) - 3| + 1)^2 - 4(1|((1x - 2)/(-3x)) - 3| + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3((3(1(-2|x| - 1)^2 + 2(-2|x| - 1) + 1) + 1)/(2(1(-2|x| - 1)^2 + 2(-2|x| - 1) + 1) + 2)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3e^(-1((-3(2x^2 - 3x - 1) + 2)/(2(2x^2 - 3x - 1) + 3))) + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-2x + 5)^2 + 4(-2x + 5) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(1(-1(-3|x - 1| - 2)^2 - 1(-3|x - 1| - 2) + 3) + 2))/(-3(1(-1(-3|x - 1| - 2)^2 - 1(-3|x - 1| - 2) + 3) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2((-1(-2e^(1(-3x - 4)) + 1) - 3)/(1(-2e^(1(-3x - 4)) + 1) + 1))^2 - 5((-1(-2e^(1(-3x - 4)) + 1) - 3)/(1(-2e^(1(-3x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(4x - 1) + 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-2|x + 3| + 1)^2 - 1(-2|x + 3| + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((3(-2(-3|x| + 3)^2 + 5(-3|x| + 3) + 5) - 1)/(1(-2(-3|x| + 3)^2 + 5(-3|x| + 3) + 5))) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3|(5(-2x^2 - 1x + 4) - 4) + 1| - 1) + 2)/(1(3|(5(-2x^2 - 1x + 4) - 4) + 1| - 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 solutions does the equation -3|(-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": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((-2x - 1)/(-3x + 2))^2 + 2((-2x - 1)/(-3x + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1((2(-3cos(2\u03c0x - 3) + 1) - 2)/(2(-3cos(2\u03c0x - 3) + 1) - 1)) + 1)^2 + 1(1((2(-3cos(2\u03c0x - 3) + 1) - 2)/(2(-3cos(2\u03c0x - 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": "How many solutions does the equation 5(-1x^2 + 4x + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1|((3x - 1)/(-3x + 4)) + 2| + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-3|x - 3|) + 2)/(-2(-3|x - 3|) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-3x)^2 + 2(-3x) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0((1(1x + 3) - 1)/(-1(1x + 3) + 2))) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(5x^2 + 1x - 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3cos(2\u03c0x - 3) - 3)^2 + 5(3cos(2\u03c0x - 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(2(-2|x + 2| + 2) + 2) - 1)/(-1(2(-2|x + 2| + 2) + 2)))^2 - 1((-3(2(-2|x + 2| + 2) + 2) - 1)/(-1(2(-2|x + 2| + 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 1cos(1\u03c0(1|x + 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": "Find the number of x-intercepts of the function f(x) = (-1(3|(1(3x - 5)^2 + 5(3x - 5) + 1) + 1|) + 2)/(-2(3|(1(3x - 5)^2 + 5(3x - 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) = -1|((1(2x^2 + 1x + 3) - 3)/(2(2x^2 + 1x + 3) + 2)) - 3| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(2|x| - 1)) - 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 3((-3x - 1)/(2x - 3))^2 - 1((-3x - 1)/(2x - 3)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(2(3x^2 + 1x - 4) + 5) + 3)/(1(2(3x^2 + 1x - 4) + 5)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-2(5(-2sin(1\u03c0x - 3))^2 + 1(-2sin(1\u03c0x - 3)) + 1) + 3)/(-3(5(-2sin(1\u03c0x - 3))^2 + 1(-2sin(1\u03c0x - 3)) + 1) - 2)) 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|(1e^(-1(-1((1x + 2)/(-1x + 3)) + 4)) - 2) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-2|(2e^(2(-3x^2 - 5x + 4))) - 3| - 1) - 2)/(-3(-2|(2e^(2(-3x^2 - 5x + 4))) - 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) = -2((1(1x + 4) - 3)/(2(1x + 4) - 1))^2 + 2((1(1x + 4) - 3)/(2(1x + 4) - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2e^(-2x) + 2)^2 + 5(-2e^(-2x) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3e^(2(-4((2x - 1)/(2x + 3))^2 + 5((2x - 1)/(2x + 3)) + 5)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((-3(1(2|x - 1| - 1)) - 1)/(-1(1(2|x - 1| - 1)) - 1))^2 + 5((-3(1(2|x - 1| - 1)) - 1)/(-1(1(2|x - 1| - 1)) - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2|(3(-2x - 4)^2 + 5(-2x - 4) - 1)| + 1))/(1(-2|(3(-2x - 4)^2 + 5(-2x - 4) - 1)| + 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 1sin(1\u03c0(-2|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": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((-1(2|(-2x + 3) - 3| + 1) + 3)/(-3(2|(-2x + 3) - 3| + 1) + 4))^2 + 2((-1(2|(-2x + 3) - 3| + 1) + 3)/(-3(2|(-2x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2(-1|((3x - 3)/(1x - 2)) - 3| + 1)^2 - 4(-1|((3x - 3)/(1x - 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": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(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": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(1((-3(-5x - 1) - 2)/(2(-5x - 1) + 1))^2 - 1((-3(-5x - 1) - 2)/(2(-5x - 1) + 1))) - 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(2|(5x^2 - 2x + 4) - 2| - 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1723", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(3x - 4)| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1(1((-2x + 3)/(-2x - 1))^2 - 1((-2x + 3)/(-2x - 1)) - 1) - 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) = 2cos(3\u03c0(-1|x - 2| - 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 solutions does the equation (1(3(-4(-1|x + 3| + 1)^2 + 5) + 4) - 3)/(2(3(-4(-1|x + 3| + 1)^2 + 5) + 4) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(3x^2 - 1) + 5) + 2)/(-3(-1(3x^2 - 1) + 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3sin(2\u03c0x + 1) - 2)^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": "Find the number of x-intercepts of the function f(x) = 1(-1((-3x + 1)/(3x - 2)) + 1)^2 - 2(-1((-3x + 1)/(3x - 2)) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(-2|((2(3x) + 3)/(2(3x) - 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": "71", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(4x + 1)^2 - 4(4x + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(3\u03c0(1x^2 + 3x - 1) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((3x - 2)/(1x - 3))^2 + 4((3x - 2)/(1x - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-2|(2cos(3\u03c0(-4x) + 1) - 3) + 2| + 3) + 3)/(3(-2|(2cos(3\u03c0(-4x) + 1) - 3) + 2| + 3) + 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": "Determine the number of values x in [-10, 10] where f(x) = (-1(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) - 3) + 2)/(-3(1(-3|x - 3| + 1)^2 - 1(-3|x - 3| + 1) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(3sin(1\u03c0(2|(-1x - 1) - 3|)) + 3))/(2(3sin(1\u03c0(2|(-1x - 1) - 3|)) + 3) - 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 1(1|((2x + 1)/(2x + 2)) - 3| - 3)^2 - 3(1|((2x + 1)/(2x + 2)) - 3| - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1(1((-3x - 3)/(-1x - 2)) + 2)^2 - 4(1((-3x - 3)/(-1x - 2)) + 2) + 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-1(-1|(-3sin(3\u03c0x - 1)) + 1| - 1)^2 + 3(-1|(-3sin(3\u03c0x - 1)) + 1| - 1) + 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "110", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(2x + 2)^2 + 2(2x + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(2|((1x)/(-1x - 2)) - 3| + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "103", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((-3(1(-2|x + 1| - 3) + 5) - 1)/(1(1(-2|x + 1| - 3) + 5) - 3))^2 + 4((-3(1(-2|x + 1| - 3) + 5) - 1)/(1(1(-2|x + 1| - 3) + 5) - 3)) - 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) = -3cos(3\u03c0(-2(1|(3x - 4) + 1| - 2)^2 - 3(1|(3x - 4) + 1| - 2) - 1) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1471", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3((-3(3(-2|x|)^2 - 2(-2|x|) - 1) - 1)/(2(3(-2|x|)^2 - 2(-2|x|) - 1))) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3x^2 + 1x + 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(1(3e^(-1(3|x - 2| - 3)) - 1)^2 + 5(3e^(-1(3|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2sin(2\u03c0x + 2))^2 + 5(-2sin(2\u03c0x + 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": "How many zeros does the function f(x) = 1(2e^(2((2x + 1)/(-1x + 2))) - 2)^2 - 4(2e^(2((2x + 1)/(-1x + 2))) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2|x + 3|) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(2|(3cos(3\u03c0(-1x^2 - 4x + 4) - 2) - 1) - 2| - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(3\u03c0(-4(4((-3x - 1)/(-2x - 2))^2 + 4((-3x - 1)/(-2x - 2)) + 1) - 4) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "427", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(1|((3x + 2)/(-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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|((-3(3sin(3\u03c0x - 1) + 2) + 2)/(2(3sin(3\u03c0x - 1) + 2) - 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 solutions does the equation 1|((-1(3sin(3\u03c0x) + 1) - 2)/(-2(3sin(3\u03c0x) + 1) - 3)) + 1| - 2 = 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": "Find the number of x-intercepts of the function f(x) = 3cos(2\u03c0(-4((-3(2x - 3) - 3)/(1(2x - 3) + 2))^2 - 2((-3(2x - 3) - 3)/(1(2x - 3) + 2)) - 5) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "214", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((-2(-2|x + 2|) - 1)/(-1(-2|x + 2|) - 1)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-3|(-1((1x)/(-1x + 2))^2 - 4((1x)/(-1x + 2)) - 1) + 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) = 5((-1(2|(-3cos(2\u03c0x + 2) + 1) + 2| - 3) + 3)/(-3(2|(-3cos(2\u03c0x + 2) + 1) + 2| - 3) - 1))^2 - 3((-1(2|(-3cos(2\u03c0x + 2) + 1) + 2| - 3) + 3)/(-3(2|(-3cos(2\u03c0x + 2) + 1) + 2| - 3) - 1)) - 5 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": "Determine the number of values x in [-10, 10] where f(x) = 2(1cos(3\u03c0(3|((-2x)/(-2x + 3)) + 1| + 2) + 1) + 1) - 1 equals zero.\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) = -2sin(1\u03c0(-2((2x - 1)/(3x - 1))^2 + 4((2x - 1)/(3x - 1)) - 1) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(3cos(1\u03c0(-5x^2 + 5x + 5) + 2) + 1) + 2)/(-1(3cos(1\u03c0(-5x^2 + 5x + 5) + 2) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "906", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-5((2(-1|x| + 2) - 3)/(1(-1|x| + 2) + 2)))^2 + 1(-5((2(-1|x| + 2) - 3)/(1(-1|x| + 2) + 2))) + 4 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(1x^2 - 2x - 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((1(-4(-2cos(2\u03c0x - 3) + 1) - 1))/(-3(-4(-2cos(2\u03c0x - 3) + 1) - 1) + 4))^2 + 4 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) = 2cos(1\u03c0(-4x - 5) - 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": "Find the number of x-intercepts of the function f(x) = 2|(-4(2x + 5)^2 - 5(2x + 5) - 2) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2x^2 - 5) - 2)/(-2(2x^2 - 5) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-2|(4x - 4) - 1| + 1) - 3)/(1(-2|(4x - 4) - 1| + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(-2(3((-1x + 1)/(2x + 2))^2 - 4((-1x + 1)/(2x + 2)) - 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3|(-1x^2 - 2x + 5) + 2|) + 1)/(-3(-3|(-1x^2 - 2x + 5) + 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) = -3sin(2\u03c0((3(-5x + 4) - 1)/(1(-5x + 4))) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(1(-1|(2cos(1\u03c0x + 1) - 2) - 3| + 3)^2 + 3) - 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": "Find the number of x-intercepts of the function f(x) = (-1(1(-3(1|x + 3| - 1) - 1)^2 - 2(-3(1|x + 3| - 1) - 1) + 2) + 3)/(-3(1(-3(1|x + 3| - 1) - 1)^2 - 2(-3(1|x + 3| - 1) - 1) + 2) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(4(-2x^2 + 3x - 2) + 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1088", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-1(-2x^2 + 5x - 4) - 4) + 2)/(2(-1(-2x^2 + 5x - 4) - 4) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(2(5x + 5)^2 - 4(5x + 5) + 5) - 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-3sin(3\u03c0(-4((-1x - 1)/(-2x - 3))^2 + 1((-1x - 1)/(-2x - 3)) + 1) - 1) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1((-2(2cos(1\u03c0x - 1) + 1))/(-1(2cos(1\u03c0x - 1) + 1) + 2)) + 5)^2 + 1(-1((-2(2cos(1\u03c0x - 1) + 1))/(-1(2cos(1\u03c0x - 1) + 1) + 2)) + 5) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(2(-1e^(-1(-2|x + 2| - 1)) + 3) + 3)^2 + 5(2(-1e^(-1(-2|x + 2| - 1)) + 3) + 3) + 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) = 3|(-3sin(1\u03c0(-3((-3x + 2)/(-1x))^2 - 5((-3x + 2)/(-1x)) - 3)) - 3) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "47", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-2sin(1\u03c0((1(-3|x| - 1) + 2)/(-1(-3|x| - 1) + 2)) + 3) + 2)^2 + 3(-2sin(1\u03c0((1(-3|x| - 1) + 2)/(-1(-3|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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((2(2|(1x + 1) + 2| - 2) + 1)/(2(2|(1x + 1) + 2| - 2) - 1))^2 - 3((2(2|(1x + 1) + 2| - 2) + 1)/(2(2|(1x + 1) + 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": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0((-2(5x + 1) - 1)/(1(5x + 1) + 3)) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(3x + 3)^2 + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2sin(1\u03c0x + 1) + 2)^2 - 3(-2sin(1\u03c0x + 1) + 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|((1x + 3)/(-1x)) - 2| + 3)^2 - 4(2|((1x + 3)/(-1x)) - 2| + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(3(5x + 5)^2 - 1(5x + 5) - 5) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1585", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0((2x - 3)/(-3x + 4)) + 3) = 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": "How many solutions does the equation 2(-3((-2(-1|x + 2| + 3) + 3)/(-2(-1|x + 2| + 3) + 1)) - 2)^2 - 5(-3((-2(-1|x + 2| + 3) + 3)/(-2(-1|x + 2| + 3) + 1)) - 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) = (3(3e^(-2(1|(-1x - 5) - 3| + 1))) - 1)/(3(3e^(-2(1|(-1x - 5) - 3| + 1))) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1|((-1(1x^2 + 5x - 1) - 1)/(-1(1x^2 + 5x - 1) + 3)) - 2| - 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) = -2sin(1\u03c0(2(2|((-2x + 1)/(-1x)) - 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": "66", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1sin(3\u03c0(2|(-1x^2 + 3x + 3) + 1|) - 1) - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1080", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3sin(2\u03c0x + 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) = -3sin(1\u03c0((3x + 1)/(-1x - 2)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0(1|(5x + 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": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(3|(-5x - 3) + 2| - 1) - 2)/(3(3|(-5x - 3) + 2| - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2cos(1\u03c0x - 2)) + 2)/(-1(2cos(1\u03c0x - 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": "Determine the number of values x in [-10, 10] where f(x) = 1((2x + 3)/(-3x + 2))^2 + 4((2x + 3)/(-3x + 2)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-1(-2|(4x + 5)| + 2)^2 + 2(-2|(4x + 5)| + 2) + 1) - 3)/(1(-1(-2|(4x + 5)| + 2)^2 + 2(-2|(4x + 5)| + 2) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-2|(-5x + 2) + 3| + 3)^2 + 4(-2|(-5x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0((-1(3(2x - 3)^2 + 2(2x - 3) - 2) - 1)/(-1(3(2x - 3)^2 + 2(2x - 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": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1|((2(-4x^2 + 3x + 5) + 2)/(-1(-4x^2 + 3x + 5) + 2)) - 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) = 1((-3x - 1)/(-2x + 3))^2 - 5((-3x - 1)/(-2x + 3)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-1sin(3\u03c0x - 3)) - 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) = (3(-2|x + 2| + 3))/(-3(-2|x + 2| + 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(-2(-1|(-1x + 1) + 3| + 3)^2 + 2(-1|(-1x + 1) + 3| + 3) + 5) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "316", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-3(3|x + 2| - 2) + 1) + 2)/(-2(-3(3|x + 2| - 2) + 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(-3x + 4) - 2) + 2 = 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) = -3e^(-1(-1(4(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 5) + 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(4((3(-2|x + 3| + 1))/(1(-2|x + 3| + 1) + 1))^2 + 3((3(-2|x + 3| + 1))/(1(-2|x + 3| + 1) + 1)) - 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 zeros does the function f(x) = -2|(5((3(-3x + 3) + 1)/(-3(-3x + 3) - 3))^2 - 1((3(-3x + 3) + 1)/(-3(-3x + 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": "Find the number of x-intercepts of the function f(x) = (3(3(1sin(3\u03c0(5x^2 + 1x - 3) - 3) + 1) - 5) - 2)/(2(3(1sin(3\u03c0(5x^2 + 1x - 3) - 3) + 1) - 5) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "987", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(1cos(1\u03c0(3(-1|x - 1| + 3) - 4) + 3))^2 - 4(1cos(1\u03c0(3(-1|x - 1| + 3) - 4) + 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": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(-2|x + 3| - 3) - 3) - 2 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) = -3((1(-2(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 2) - 2)/(-3(-2(1|x + 3| + 2)^2 + 4(1|x + 3| + 2) + 2) - 3)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((3(-1|(2x^2 - 5x) - 1| + 2))/(-2(-1|(2x^2 - 5x) - 1| + 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) = 1e^(1(1|x - 1| - 2)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1(3|(5x - 1) - 3| - 1)^2 + 3(3|(5x - 1) - 3| - 1) + 2) + 2)/(2(1(3|(5x - 1) - 3| - 1)^2 + 3(3|(5x - 1) - 3| - 1) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0(3((2x + 2)/(-2x + 3))^2 + 4((2x + 2)/(-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": "231", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(3\u03c0(-1((1(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1))) - 4) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(1\u03c0((-3(-1(-1x - 3)^2 - 4(-1x - 3) + 3) + 1)/(1(-1(-1x - 3)^2 - 4(-1x - 3) + 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": "85", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(3sin(2\u03c0x - 1)) + 3)/(-1(3sin(2\u03c0x - 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": "Find the number of x-intercepts of the function f(x) = -1|(2e^(-2x) - 1) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(1cos(1\u03c0(4x - 2) + 3)))/(3(1cos(1\u03c0(4x - 2) + 3)) - 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) = (-1(2x^2 - 4x - 3) + 2)/(1(2x^2 - 4x - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1sin(1\u03c0x) + 1) 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 -4((-1(3|(4x^2 + 4x - 3) + 2| - 3) - 1)/(-1(3|(4x^2 + 4x - 3) + 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": "Find the number of x-intercepts of the function f(x) = 3|((2(-2(-2x^2 + 3x - 1) - 2) - 1)/(3(-2(-2x^2 + 3x - 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": "Find the number of x-intercepts of the function f(x) = 3(-2|(2((-2x)/(1x + 3)) - 4) - 1| + 3)^2 + 3(-2|(2((-2x)/(1x + 3)) - 4) - 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": "How many solutions does the equation (-1(1|(2cos(3\u03c0x + 3))| - 1))/(1(1|(2cos(3\u03c0x + 3))| - 1) + 2) = 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(2(-4x + 5)^2 - 4(-4x + 5) - 2))/(-2(2(-4x + 5)^2 - 4(-4x + 5) - 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((1(-3x + 5) - 2)/(2(-3x + 5) - 3))^2 - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1e^(-2x) - 2) - 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(3|x + 2| - 2)^2 + 3(3|x + 2| - 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": "Determine the number of values x in [-10, 10] where f(x) = 5(3|((1(-3x - 1) + 3)/(2(-3x - 1) + 2)) - 2| - 3)^2 - 1(3|((1(-3x - 1) + 3)/(2(-3x - 1) + 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": "Find the number of x-intercepts of the function f(x) = (2(-2|(-3x - 5) + 2| + 3))/(1(-2|(-3x - 5) + 2| + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-1|(5((-3x + 3)/(-3x)) + 3)| + 2) + 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": "How many solutions does the equation -3((-3(-3|(1x - 3) - 1| + 3) + 2)/(-1(-3|(1x - 3) - 1| + 3) + 2))^2 + 2((-3(-3|(1x - 3) - 1| + 3) + 2)/(-1(-3|(1x - 3) - 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 1(3cos(2\u03c0(-3x - 2) - 3) - 3)^2 - 3(3cos(2\u03c0(-3x - 2) - 3) - 3) - 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 2cos(2\u03c0((3x + 3)/(1x)) + 1) + 2 = 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": "Determine the number of values x in [-10, 10] where f(x) = 5(3|(3cos(3\u03c0((-3x + 3)/(3x - 2)) + 1)) + 3| - 1) + 3 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) = (-2(-1|(-3cos(3\u03c0x - 3) + 2)| + 2) - 3)/(2(-1|(-3cos(3\u03c0x - 3) + 2)| + 2) - 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(-1cos(1\u03c0x - 3) - 3)^2 + 4) - 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": "How many solutions does the equation 4(1|(-1((2x - 2)/(3x - 1)) - 5)|)^2 - 1(1|(-1((2x - 2)/(3x - 1)) - 5)|) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-5x) - 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-2(4(2|x + 3| - 3) + 2)^2 - 1(4(2|x + 3| - 3) + 2) + 5) + 3)/(-1(-2(4(2|x + 3| - 3) + 2)^2 - 1(4(2|x + 3| - 3) + 2) + 5) + 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 2cos(3\u03c0(2|(-4x^2 - 5x - 5) + 3| + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1623", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(4(-2sin(1\u03c0x + 2)) + 4) + 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(2(-5(-3cos(3\u03c0x - 3) - 1) + 2)^2 + 5(-5(-3cos(3\u03c0x - 3) - 1) + 2) + 1) - 2| + 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": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0(-4(-3|x - 3| - 2)^2 + 3(-3|x - 3| - 2) - 4) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1199", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-5x^2 - 3x) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3x - 3)^2 - 5(3x - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(1(3(-1cos(1\u03c0x + 3)) - 1)^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": "How many solutions does the equation 3(-2x)^2 + 4(-2x) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|((3(4(-4x^2 - 2x + 4) - 4) + 1)/(-1(4(-4x^2 - 2x + 4) - 4) + 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": "Determine the number of values x in [-10, 10] where f(x) = 3e^(1((-3(1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3)) + 3)/(-1(1(-2|x + 1| + 3)^2 - 3(-2|x + 1| + 3)) + 2))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(2\u03c0(-2|(4((1x - 3)/(2x - 1))^2 - 2((1x - 3)/(2x - 1)) + 4) - 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": "132", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-5((-2x - 3)/(2x))^2 - 1((-2x - 3)/(2x)) + 4) - 1| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1((-1(3|x + 1| - 3) - 2)/(-3(3|x + 1| - 3) + 4))^2 + 5((-1(3|x + 1| - 3) - 2)/(-3(3|x + 1| - 3) + 4)) + 4) + 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) = 4(2|(4x^2 - 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": "How many zeros does the function f(x) = 1(-3(-1cos(3\u03c0x))^2 - 1(-1cos(3\u03c0x)) + 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": "How many solutions does the equation (1(-3|(-2(-1cos(2\u03c0x - 2) - 1)^2 + 1(-1cos(2\u03c0x - 2) - 1) + 5) + 1| + 3) + 3)/(-3(-3|(-2(-1cos(2\u03c0x - 2) - 1)^2 + 1(-1cos(2\u03c0x - 2) - 1) + 5) + 1| + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(2(2|((-1x + 2)/(-1x)) + 1|))^2 + 3(2(2|((-1x + 2)/(-1x)) + 1|)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((1(-2(-3|x - 1| + 3) - 5) - 3)/(3(-2(-3|x - 1| + 3) - 5)))^2 + 1((1(-2(-3|x - 1| + 3) - 5) - 3)/(3(-2(-3|x - 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": "Determine the number of values x in [-10, 10] where f(x) = (2(-4(2|(-1x - 1) - 1|)^2 - 4(2|(-1x - 1) - 1|) + 4))/(2(-4(2|(-1x - 1) - 1|)^2 - 4(2|(-1x - 1) - 1|) + 4) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((-2(1x^2 + 4x - 2) + 2)/(-3(1x^2 + 4x - 2) - 2)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(3(-1|((2x - 3)/(3x + 3)) + 1| - 2)^2 + 5(-1|((2x - 3)/(3x + 3)) + 1| - 2) - 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-3((3x - 2)/(-2x + 3))^2 - 2((3x - 2)/(-2x + 3)) + 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0(-1|(2x^2 - 4x - 4) - 3|)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2e^(-2(-2((-2x + 2)/(-3x))^2 + 3)) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3((-3(-5x + 4) - 1)/(-1(-5x + 4) - 3))^2 + 3((-3(-5x + 4) - 1)/(-1(-5x + 4) - 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|((2(-5x^2 + 5x + 3) + 2)/(2(-5x^2 + 5x + 3) - 1)) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2sin(3\u03c0(-4(3|x - 2| + 2) + 3) - 1) - 2)^2 + 3(-2sin(3\u03c0(-4(3|x - 2| + 2) + 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": "720", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1cos(3\u03c0(-2|x - 2| - 3)) - 1)^2 - 2(-1cos(3\u03c0(-2|x - 2| - 3)) - 1) + 4 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(-2cos(3\u03c0x - 2) - 2) + 3)/(-1(-2cos(3\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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|x + 3|)^2 + 3(2|x + 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) = (-2(3|(2(-5x + 4)^2 - 2(-5x + 4) - 3) - 3| - 2) + 3)/(2(3|(2(-5x + 4)^2 - 2(-5x + 4) - 3) - 3| - 2) + 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(-2|(-3cos(3\u03c0x - 3) - 2)| + 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 zeros does the function f(x) = -1((-1(2sin(2\u03c0x + 2) + 1) + 2)/(-2(2sin(2\u03c0x + 2) + 1)))^2 - 2((-1(2sin(2\u03c0x + 2) + 1) + 2)/(-2(2sin(2\u03c0x + 2) + 1))) + 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": "How many solutions does the equation 1(2(3|((2x + 3)/(3x + 3)) - 3| + 1)^2 - 4(3|((2x + 3)/(3x + 3)) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1e^(-1(2x^2 - 5x - 1)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(1((-2(3x - 4) + 3)/(3(3x - 4) + 3))^2 + 5((-2(3x - 4) + 3)/(3(3x - 4) + 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 zeros does the function f(x) = 2((3(-2(3|x + 3| + 1) + 5) - 3)/(1(-2(3|x + 3| + 1) + 5) + 2))^2 + 4((3(-2(3|x + 3| + 1) + 5) - 3)/(1(-2(3|x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-3sin(3\u03c0x - 3) + 3) + 2| + 2 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": "How many solutions does the equation 2sin(1\u03c0((-1x + 3)/(-3x + 1)) - 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = 2|(-4(-2((2x + 1)/(-3x + 2)))^2 + 3) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((1x - 1)/(2x - 1))^2 - 5((1x - 1)/(2x - 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2e^(2(-3(1|(4x + 4) - 2| + 2)^2 + 1(1|(4x + 4) - 2| + 2) - 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-2(2|(-5x^2 - 1x - 3) - 1| - 3) + 3) + 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1159", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1sin(2\u03c0x - 2) + 1) - 2)/(2(-1sin(2\u03c0x - 2) + 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) = 4(-3|x + 2| + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1(5(-2|x - 1| + 3)^2 - 3(-2|x - 1| + 3) - 1) - 5) - 1)/(2(1(5(-2|x - 1| + 3)^2 - 3(-2|x - 1| + 3) - 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": "How many solutions does the equation -1|(3sin(2\u03c0(-3x^2 + 5x) - 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": "1128", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3x + 5)^2 + 2(-3x + 5) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-2|x + 3| + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2e^(1(4(5(-1|x - 2| + 3)^2 - 5(-1|x - 2| + 3) - 3) + 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) = -4(-2|(-4((-2x - 3)/(-3x - 1))^2 - 5((-2x - 3)/(-3x - 1)) + 5) + 1| + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(3sin(2\u03c0x - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1((-2x - 1)/(1x + 3))^2 - 1) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(4x^2 + 1x - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-3|x + 1| + 3)^2 + 4(-3|x + 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) = 5(4x - 1)^2 + 3(4x - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1cos(3\u03c0x - 1) - 3) + 3)/(2(1cos(3\u03c0x - 1) - 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": "Find the number of x-intercepts of the function f(x) = -5(1|((1(-2x^2 + 3x + 2) - 2)/(3(-2x^2 + 3x + 2) - 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": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0((1x - 3)/(2x)) + 3) - 1 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 -4(2x - 1)^2 - 2(2x - 1) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-2|((-1x)/(1x + 1)) + 2| + 2)^2 + 2(-2|((-1x)/(1x + 1)) + 2| + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(3|x + 1|) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(-5((2x + 3)/(2x - 1))^2 - 4((2x + 3)/(2x - 1)) - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "282", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(3(-1sin(3\u03c0(2|x - 1| - 3) + 1) - 1)^2 - 5(-1sin(3\u03c0(2|x - 1| - 3) + 1) - 1) - 2))/(2(3(-1sin(3\u03c0(2|x - 1| - 3) + 1) - 1)^2 - 5(-1sin(3\u03c0(2|x - 1| - 3) + 1) - 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": "How many solutions does the equation -1|((-3(5(-1x - 5)^2 - 5(-1x - 5) + 2) + 2)/(-1(5(-1x - 5)^2 - 5(-1x - 5) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(-5(2|x - 1| - 1) - 4) - 2) - 1 equals zero.\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) = -1|(-4(-3cos(1\u03c0(-2x - 4)) + 3)^2 - 3(-3cos(1\u03c0(-2x - 4)) + 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": "Determine the number of values x in [-10, 10] where f(x) = -2|(3(1sin(2\u03c0x + 3) - 2)^2 - 3(1sin(2\u03c0x + 3) - 2) - 2) - 3| + 3 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 -3|((2(-1x^2 + 5x + 4) - 2)/(3(-1x^2 + 5x + 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": "How many zeros does the function f(x) = -5(-1|(-3(1cos(1\u03c0x - 2) + 1) - 1) - 1| + 1)^2 - 2(-1|(-3(1cos(1\u03c0x - 2) + 1) - 1) - 1| + 1) + 4 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) = 3e^(1(-3((3x - 3)/(2x))^2 - 1((3x - 3)/(2x)) + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-1|((-2(-4x - 2))/(1(-4x - 2) + 3)) + 1| + 1)^2 + 1(-1|((-2(-4x - 2))/(1(-4x - 2) + 3)) + 1| + 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0((1(-3x + 5) - 2)/(-3(-3x + 5) + 4)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-2|x + 3| + 2) - 2)/(2(-2|x + 3| + 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-1(-2e^(2(-1x + 1)) + 3)^2 - 5(-2e^(2(-1x + 1)) + 3) + 5) - 1)/(-1(-1(-2e^(2(-1x + 1)) + 3)^2 - 5(-2e^(2(-1x + 1)) + 3) + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(2\u03c0((-1x + 2)/(-1x)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1|(-3x - 4) + 1| + 3)^2 - 5(-1|(-3x - 4) + 1| + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(3sin(2\u03c0((2(4x^2 + 1x - 5))/(2(4x^2 + 1x - 5) - 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": "24", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-5(2|x - 3|) + 1))/(-1(-5(2|x - 3|) + 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(3cos(2\u03c0(-1|x + 2| - 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 (-2(-2|(-1cos(1\u03c0x + 3) - 1) + 2| + 1) + 1)/(3(-2|(-1cos(1\u03c0x + 3) - 1) + 2| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3|(-1((-2x - 3)/(2x - 3))) + 1| - 2)^2 + 3(3|(-1((-2x - 3)/(2x - 3))) + 1| - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-2((1(-1x) - 3)/(3(-1x) + 2))^2 - 1((1(-1x) - 3)/(3(-1x) + 2)) - 3) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(5(3sin(2\u03c0x - 2) - 1) + 4) - 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) = 4(5((1(-2|x + 1| - 1) - 2)/(2(-2|x + 1| - 1) - 1)) - 5)^2 + 2(5((1(-2|x + 1| - 1) - 2)/(2(-2|x + 1| - 1) - 1)) - 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2|((2x + 3)/(-3x + 1)) - 2| - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(2sin(3\u03c0(-1|x + 2| - 3) - 2) + 1) - 2)/(-2(2sin(3\u03c0(-1|x + 2| - 3) - 2) + 1) - 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": "Determine the number of values x in [-10, 10] where f(x) = 1|(-5(2cos(1\u03c0((2x - 3)/(-1x - 1)) - 2) - 2)^2 + 2(2cos(1\u03c0((2x - 3)/(-1x - 1)) - 2) - 2) + 1)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2e^(-1(-3((-3(-1|x + 1| + 1))/(2(-1|x + 1| + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-2|(-5(3sin(1\u03c0x) - 2) - 1)| + 2) + 1)/(1(-2|(-5(3sin(1\u03c0x) - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(1(-5x^2 + 2x - 2) + 5) + 2)/(1(1(-5x^2 + 2x - 2) + 5)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2((-3(-1x - 4))/(-2(-1x - 4) + 3))^2 + 4((-3(-1x - 4))/(-2(-1x - 4) + 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(3sin(3\u03c0x - 1) - 1))/(-3(3sin(3\u03c0x - 1) - 1) - 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 (2(-2|(1x - 4) - 1| + 1) + 1)/(-2(-2|(1x - 4) - 1| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(1|x + 2|) + 2)/(2(1|x + 2|) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0(-1|(-5x^2 - 4) - 1| + 2) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1316", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(1(-5x^2 + 4x + 1) + 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 zeros does the function f(x) = 1(-5x^2 + 4x - 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(-4x^2 - 4x - 4) + 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1310", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(5(-2|x + 2| + 1)^2 - 3(-2|x + 2| + 1) - 5) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(1(2((-2x + 1)/(-2x - 1))^2 - 1((-2x + 1)/(-2x - 1)) - 4) + 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 zeros does the function f(x) = -2|(1((2x + 1)/(-2x + 3))^2 + 2((2x + 1)/(-2x + 3)) - 5) - 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) = 2|(5(3cos(3\u03c0x + 3) - 2)^2 + 2(3cos(3\u03c0x + 3) - 2) - 4) + 1| - 2 equals zero.\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) = (2(1(2x - 4)^2 + 1(2x - 4) - 5))/(3(1(2x - 4)^2 + 1(2x - 4) - 5) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0((2(-2|x - 1| + 3) - 1)/(2(-2|x - 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": "70", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3e^(1(-1|((-2x - 2)/(2x + 3)) - 1| + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(-3(3|x| + 1) + 5) - 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "176", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1|x - 3| + 3)^2 + 2(-1|x - 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 zeros does the function f(x) = -3sin(2\u03c0(2|(-5x + 4) - 3| + 2) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2((-1x - 3)/(-1x))^2 + 3((-1x - 3)/(-1x)) - 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(-5(3|x + 2|)^2 - 2(3|x + 2|) + 3) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1207", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(4((3(-3e^(-1x) + 3) + 2)/(-1(-3e^(-1x) + 3) + 3))^2 + 4((3(-3e^(-1x) + 3) + 2)/(-1(-3e^(-1x) + 3) + 3)) - 2) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-3cos(2\u03c0((-3x + 2)/(1x - 3)) - 3) - 1)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2|x - 1| + 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-1x^2 - 5x - 1) + 1)/(-2(-1x^2 - 5x - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3((2(-1sin(2\u03c0x + 1) - 2) + 3)/(-1(-1sin(2\u03c0x + 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 solutions does the equation 1sin(3\u03c0(-2|(1((1x + 3)/(-1x - 2))^2 - 1((1x + 3)/(-1x - 2)) - 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": "82", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-3e^(2((-1(-3x - 5))/(3(-3x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((2x - 1)/(-3x + 1))^2 + 1((2x - 1)/(-3x + 1)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(3((2x + 3)/(-3x - 3)) + 4)^2 + 1(3((2x + 3)/(-3x - 3)) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(4(-2x^2 - 2x + 2) - 1) - 2)/(2(4(-2x^2 - 2x + 2) - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3|(3(-2x - 5)^2 + 2(-2x - 5) + 1) - 2|))/(-2(3|(3(-2x - 5)^2 + 2(-2x - 5) + 1) - 2|) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1cos(3\u03c0x + 3)) + 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": "Find the number of x-intercepts of the function f(x) = 1sin(1\u03c0(3|x| - 1) + 2) - 1 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": "How many zeros does the function f(x) = 4(2e^(-1x) - 1)^2 - 5(2e^(-1x) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(2x + 2) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(-1x^2 + 3x - 3)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "611", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-1|(-3cos(1\u03c0x + 2) + 1) - 3|)^2 - 5(-1|(-3cos(1\u03c0x + 2) + 1) - 3|) have in the interval [-10, 10]?\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) = (1(3|(5(-2x^2 - 2x + 5) + 1) + 2| + 1) - 3)/(2(3|(5(-2x^2 - 2x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(4(1e^(-2(-5x^2 + 2x)) - 3) + 2)| + 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) = -3cos(2\u03c0((1x - 1)/(2x - 1)) - 3) + 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) = 3sin(2\u03c0(-2x - 5)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-1sin(1\u03c0x + 2) + 1) - 2)/(-1(-1sin(1\u03c0x + 2) + 1) - 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) = 3(3(2|x + 1| - 3) - 3)^2 - 2(3(2|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": "Find the number of x-intercepts of the function f(x) = -2|(5(-5((-3x - 1)/(-1x - 1))^2 - 4((-3x - 1)/(-1x - 1)) + 1) - 3) - 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0((1(3|(1x - 1) - 2| + 1) + 3)/(-1(3|(1x - 1) - 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": "48", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(1x^2 - 3x + 1) + 1)/(-3(1x^2 - 3x + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-3sin(2\u03c0(-1(-3|x - 1| - 3)^2 - 2) - 3) - 1) - 2)/(-2(-3sin(2\u03c0(-1(-3|x - 1| - 3)^2 - 2) - 3) - 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "407", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0((-3(1(2|x + 1| - 2) + 3) + 1)/(2(1(2|x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-2x)^2 + 5(-2x) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2|x - 3| - 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2sin(2\u03c0(-1|((1x + 3)/(3x + 3)) + 2| - 1) - 2) + 1)^2 - 5(2sin(2\u03c0(-1|((1x + 3)/(3x + 3)) + 2| - 1) - 2) + 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) = -3cos(1\u03c0(-1(-4x^2 + 3x - 2) + 5) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "755", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-5x^2 - 2x + 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 (-3(3(2|(-2cos(3\u03c0x + 2) - 1)| - 3) + 2))/(-1(3(2|(-2cos(3\u03c0x + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(-3x^2 + 2) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-2((3(-3|x - 1|) + 1)/(1(-3|x - 1|)))^2 - 5((3(-3|x - 1|) + 1)/(1(-3|x - 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) = 5((2(-3|(-2x - 2) + 3| - 1))/(-3(-3|(-2x - 2) + 3| - 1) + 2))^2 + 3((2(-3|(-2x - 2) + 3| - 1))/(-3(-3|(-2x - 2) + 3| - 1) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0((1(1x) - 3)/(-2(1x) - 3)) - 3) + 1 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) = 1|((-1(3(-2sin(1\u03c0x + 2) + 2)^2 - 5(-2sin(1\u03c0x + 2) + 2) + 2) - 2)/(1(3(-2sin(1\u03c0x + 2) + 2)^2 - 5(-2sin(1\u03c0x + 2) + 2) + 2) - 2))| - 1 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(1|x - 3| - 2) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-1|(3cos(1\u03c0x + 3)) - 3| + 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": "Determine the number of values x in [-10, 10] where f(x) = (1(3x^2 - 4x - 5) + 1)/(-2(3x^2 - 4x - 5) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-1e^(1x)) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2e^(1(1|(1((-2x - 1)/(2x - 1)) - 2) + 1|)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-2sin(3\u03c0x - 1) - 1) - 1)/(-1(-2sin(3\u03c0x - 1) - 1) - 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) = -1(1|(1((-1x)/(3x + 3))) - 3| + 1)^2 + 5(1|(1((-1x)/(3x + 3))) - 3| + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(-2|(-1x^2 - 4x - 2) + 2| + 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "358", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-4(-1x^2 + 2x + 4) - 2) + 3)/(-2(-4(-1x^2 + 2x + 4) - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|((2(-2x + 1) - 3)/(3(-2x + 1) + 1)) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(-3((3x + 2)/(3x - 1)) - 4) - 3) 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(3(5(1|x - 2| - 1)^2 + 1(1|x - 2| - 1) - 5) - 2))/(3(3(5(1|x - 2| - 1)^2 + 1(1|x - 2| - 1) - 5) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(1|(4((-1x - 3)/(-1x + 3))^2 - 5((-1x - 3)/(-1x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-5x)^2 + 1(-5x) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1e^(-2((-3(1(2x + 1)^2 + 1(2x + 1) - 1) + 3)/(3(1(2x + 1)^2 + 1(2x + 1) - 1) - 2))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-1(4(2sin(2\u03c0x - 2) - 2)^2)) + 3)/(1(-1(4(2sin(2\u03c0x - 2) - 2)^2)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(3cos(3\u03c0x - 3) + 1) + 3)/(-3(3cos(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": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-2sin(3\u03c0x - 2) - 2))/(1(-2sin(3\u03c0x - 2) - 2) - 2) 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 5(-1|x - 3| + 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(-3|(-5(3x^2 - 5x - 5) - 4) - 1|) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1457", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(4(-3x^2 - 1x + 3)) + 1)/(3(4(-3x^2 - 1x + 3)) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-1(1e^(-1((-1x + 3)/(-3x))) + 3) + 5)^2 - 4(-1(1e^(-1((-1x + 3)/(-3x))) + 3) + 5) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3e^(-1(-1|(1x^2 + 4x - 3) + 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) = 1sin(2\u03c0(-2x - 3) - 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": "How many solutions does the equation (-3(5x^2 - 3x - 1) + 1)/(-1(5x^2 - 3x - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(3\u03c0(-1|((-2(4x - 1) - 1)/(2(4x - 1) - 1))| - 1) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-2(-3sin(1\u03c0x - 2) - 1) - 2)/(-2(-3sin(1\u03c0x - 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2e^(2(2|(1x + 5)| - 2)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1(1(2|x - 2| - 3) - 5)^2 - 4(1(2|x - 2| - 3) - 5)) + 1)/(2(1(1(2|x - 2| - 3) - 5)^2 - 4(1(2|x - 2| - 3) - 5))) 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|((2x - 3)/(-1x + 2)) - 1| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(2|(2x^2 + 3x - 1) - 2| - 2) + 1)/(2(2|(2x^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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(2|(-4x^2 + 4x + 3) + 2|)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1670", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-2(1e^(-1((-2x)/(1x + 2))) - 2)^2 + 4(1e^(-1((-2x)/(1x + 2))) - 2) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(1((-3x - 2)/(1x + 3))^2 + 3((-3x - 2)/(1x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(2(-1x^2 - 5x + 3) - 1) - 1)/(-2(2(-1x^2 - 5x + 3) - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(2(-4(1e^(1x) - 2) - 3)^2 + 5(-4(1e^(1x) - 2) - 3) - 2) - 2)/(-2(2(-4(1e^(1x) - 2) - 3)^2 + 5(-4(1e^(1x) - 2) - 3) - 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((2(-1sin(3\u03c0x + 3)) - 2)/(1(-1sin(3\u03c0x + 3)) + 1)) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2e^(1((-3(3|(-5x + 4) + 1| - 3))/(-3(3|(-5x + 4) + 1| - 3) + 2))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-2((-2(1x - 3) - 1)/(-1(1x - 3) - 3))^2 - 5((-2(1x - 3) - 1)/(-1(1x - 3) - 3))) + 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) = 1|((3x + 1)/(2x + 3)) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((1(5x^2 - 4x - 2) - 2)/(-2(5x^2 - 4x - 2) - 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(1|(1sin(1\u03c0x - 3) + 2) - 1| + 2) - 3)/(-3(1|(1sin(1\u03c0x - 3) + 2) - 1| + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-3|x - 3| + 1)^2 + 4(-3|x - 3| + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-5(3cos(3\u03c0(1x^2 + 5x) - 1))) - 1)/(2(-5(3cos(3\u03c0(1x^2 + 5x) - 1))) - 3) = 0 have in the range [-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 1(3|x - 2| - 2)^2 - 1(3|x - 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": "How many solutions does the equation 1cos(2\u03c0(4((-1(-2x^2 + 2x + 3) - 3)/(3(-2x^2 + 2x + 3))) + 1) + 2) = 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": "How many solutions does the equation 2(1(1e^(1((3x - 3)/(1x))) - 2) - 1)^2 - 2(1(1e^(1((3x - 3)/(1x))) - 2) - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2|((-2(-5x - 3) + 3)/(1(-5x - 3) + 2))|)^2 + 3(2|((-2(-5x - 3) + 3)/(1(-5x - 3) + 2))|) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-3|x + 2| + 1) + 3)/(3(-3|x + 2| + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2cos(2\u03c0(3x - 2) + 2) - 1) - 1)/(1(2cos(2\u03c0(3x - 2) + 2) - 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) = 2sin(2\u03c0((-3x + 3)/(1x + 3)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "111", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(5((2(-2|x - 3| + 1) + 1)/(-1(-2|x - 3| + 1) + 2)))^2 + 1(5((2(-2|x - 3| + 1) + 1)/(-1(-2|x - 3| + 1) + 2))) - 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 solutions does the equation (2(1(3|(-2x^2 + 3) + 3|)))/(-1(1(3|(-2x^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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(-1|(-1x - 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) = 1|(3x^2 - 5x + 2) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1(-5x^2 + 4x + 1) + 3) - 2)/(-1(1(-5x^2 + 4x + 1) + 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0((-3x)/(-2x + 3))) - 1 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": "Find the number of x-intercepts of the function f(x) = -3cos(2\u03c0(-3|x - 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": "How many solutions does the equation 3cos(3\u03c0((3x - 3)/(-1x - 3)) - 2) + 3 = 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": "Determine the number of values x in [-10, 10] where f(x) = 2sin(3\u03c0(-3|(-2((-1x + 3)/(2x - 3))^2 + 4((-1x + 3)/(2x - 3)) - 2) + 1| + 1) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "175", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(1(-2|(-4x^2 + 2x + 5) + 2| + 1) + 2) - 2)/(-1(1(-2|(-4x^2 + 2x + 5) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((2(3|(-3sin(2\u03c0x - 2) - 1) + 2| + 1) - 1)/(1(3|(-3sin(2\u03c0x - 2) - 1) + 2| + 1) + 3))^2 + 1((2(3|(-3sin(2\u03c0x - 2) - 1) + 2| + 1) - 1)/(1(3|(-3sin(2\u03c0x - 2) - 1) + 2| + 1) + 3)) + 5 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 -3cos(1\u03c0(-2|x + 1| + 1) + 1) - 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 solutions does the equation -2sin(1\u03c0(5x^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": "951", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(1sin(3\u03c0x - 2) + 2) - 2)/(1(1sin(3\u03c0x - 2) + 2) - 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(2(-3|x + 3| + 1)^2 - 5(-3|x + 3| + 1) - 2) + 3)/(-1(2(-3|x + 3| + 1)^2 - 5(-3|x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((-2(2sin(3\u03c0(-1|x - 2| - 3) + 3) + 1))/(1(2sin(3\u03c0(-1|x - 2| - 3) + 3) + 1) + 1))^2 + 5((-2(2sin(3\u03c0(-1|x - 2| - 3) + 3) + 1))/(1(2sin(3\u03c0(-1|x - 2| - 3) + 3) + 1) + 1)) + 5 equals zero.\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) = -3cos(2\u03c0(-4(4((3x + 1)/(-1x + 2))^2 + 1((3x + 1)/(-1x + 2)) + 1) - 4) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "886", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1e^(-1(-2|x - 2| + 3)) - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-3(1cos(1\u03c0x + 3)) - 3) + 2| + 3 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) = -5(2sin(2\u03c0(1|x| - 1) - 1) - 3)^2 - 4(2sin(2\u03c0(1|x| - 1) - 1) - 3) + 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": "Find the number of x-intercepts of the function f(x) = 1|(-2(-5((3x + 2)/(1x - 3))^2 + 3((3x + 2)/(1x - 3)) + 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) = 1cos(3\u03c0(3((1x - 3)/(3x + 2))^2 + 5((1x - 3)/(3x + 2)) + 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-2e^(2x) + 2) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-1x^2 + 2x + 1) - 1)/(3(-1x^2 + 2x + 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2((-3(1|(-1x + 3) - 2| - 1) - 2)/(2(1|(-1x + 3) - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2(3|x + 3|) - 4)^2 + 3(2(3|x + 3|) - 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) = -3cos(2\u03c0((3x - 1)/(-3x - 3)) + 1) + 2 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": "How many zeros does the function f(x) = 2|(2cos(3\u03c0((-1(-3x^2 - 2x - 3) - 1)/(-2(-3x^2 - 2x - 3))) - 3) - 2) + 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) = -3|((2(-3(5x + 3)^2 - 2(5x + 3) + 3) - 2)/(-2(-3(5x + 3)^2 - 2(5x + 3) + 3) + 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": "How many solutions does the equation (1(-5x^2 + 2x + 2) - 1)/(-3(-5x^2 + 2x + 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|((-2(-3cos(1\u03c0(-4x) + 3) - 3))/(-3(-3cos(1\u03c0(-4x) + 3) - 3) - 2)) + 3| - 2 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) = -3|(4(4x^2 + 3x - 4) + 5) - 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 zeros does the function f(x) = (-1(1(-1(-3|x + 2|)^2 + 4(-3|x + 2|) + 1) + 5) - 2)/(3(1(-1(-3|x + 2|)^2 + 4(-3|x + 2|) + 1) + 5) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(2|(1((-3x)/(1x - 2)) + 2) - 2| - 1)^2 + 5(2|(1((-3x)/(1x - 2)) + 2) - 2| - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-2(5(2cos(3\u03c0x + 3) - 1)^2 + 1(2cos(3\u03c0x + 3) - 1) - 3) + 3)/(1(5(2cos(3\u03c0x + 3) - 1)^2 + 1(2cos(3\u03c0x + 3) - 1) - 3) + 2)) - 4 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) = -2e^(-1(-3(-5x^2 - 1x + 2))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2cos(1\u03c0(-3|x - 3| - 1) + 3) - 3)^2 - 2(2cos(1\u03c0(-3|x - 3| - 1) + 3) - 3) 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(-3x^2 + 4x) + 3)/(-1(-3x^2 + 4x) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-2(2|x + 2| - 2) - 2) + 3)/(-1(-2(2|x + 2| - 2) - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(1(-1|(-1x^2 + 1x + 5) + 2| + 2)) - 2)/(-2(1(-1|(-1x^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": "How many zeros does the function f(x) = 5(-2e^(-2(-4(-1|x - 2| + 2)^2 - 2(-1|x - 2| + 2) + 1)) + 3) + 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(1(-2|x + 3|)^2 - 2(-2|x + 3|) - 4) + 1)/(3(1(-2|x + 3|)^2 - 2(-2|x + 3|) - 4) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-1(3cos(1\u03c0(-1x^2 - 3x - 4) - 2) - 3) - 2)/(-3(3cos(1\u03c0(-1x^2 - 3x - 4) - 2) - 3) - 3)) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "261", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-2cos(3\u03c0x + 2) + 1) - 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) = -3(-3cos(1\u03c0x + 2) - 2) 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(-2|x + 3| + 1)^2 - 4(-2|x + 3| + 1) - 5) - 1)/(-2(1(-2|x + 3| + 1)^2 - 4(-2|x + 3| + 1) - 5) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(3e^(-1((-3x + 3)/(-1x - 2))) - 3)^2 + 3(3e^(-1((-3x + 3)/(-1x - 2))) - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(2cos(1\u03c0((2(3|x - 2| + 1) + 1)/(-1(3|x - 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": "108", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(1\u03c0(-3|(5((-1x)/(3x - 1))^2 - 5((-1x)/(3x - 1)) - 4) - 3| - 3) + 2) - 1 equals zero.\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) = 3(4((2(-1|x| + 2) + 3)/(2(-1|x| + 2) + 2))^2 + 4((2(-1|x| + 2) + 3)/(2(-1|x| + 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": "How many solutions does the equation (-3(4x^2 - 5) + 1)/(-3(4x^2 - 5) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|x + 3| + 2)^2 - 5(-3|x + 3| + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(1(3cos(2\u03c0x) + 1) - 1) - 2)/(-2(1(3cos(2\u03c0x) + 1) - 1) - 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 2sin(3\u03c0(1((-2x - 3)/(-3x - 2)) - 4)) = 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 solutions does the equation (-3(1sin(1\u03c0(-3|(4x^2 - 5x + 5) - 3| - 2) - 1) - 1) - 3)/(-2(1sin(1\u03c0(-3|(4x^2 - 5x + 5) - 3| - 2) - 1) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "851", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-3x^2 + 3x + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(2(-1((2x + 3)/(-2x - 2))^2 + 4) - 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": "How many zeros does the function f(x) = 2|(1cos(1\u03c0x + 1) - 3) + 1| - 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": "How many zeros does the function f(x) = 2(3((-1(1cos(1\u03c0x + 1) + 1) + 1)/(-2(1cos(1\u03c0x + 1) + 1) - 2)))^2 + 3(3((-1(1cos(1\u03c0x + 1) + 1) + 1)/(-2(1cos(1\u03c0x + 1) + 1) - 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) = -3((-3(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2))^2 - 5((-3(-2|x + 2| + 1) - 1)/(3(-2|x + 2| + 1) - 2)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(2x^2 - 1) + 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(2(-3|x + 3| - 2)^2 - 2(-3|x + 3| - 2) + 4) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1450", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1|((-1(-2x^2 + 5x + 5))/(-3(-2x^2 + 5x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-1(-3x - 5)^2 - 3(-3x - 5) + 5) - 3)/(2(-1(-3x - 5)^2 - 3(-3x - 5) + 5) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((-3(2cos(1\u03c0x) + 1) - 3)/(3(2cos(1\u03c0x) + 1) - 2)) - 2 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) = (3(-4(-3cos(3\u03c0x - 2) + 1)^2 - 1(-3cos(3\u03c0x - 2) + 1) + 1) - 1)/(2(-4(-3cos(3\u03c0x - 2) + 1)^2 - 1(-3cos(3\u03c0x - 2) + 1) + 1) + 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 2((-3(-2cos(1\u03c0x - 1) + 1) + 3)/(-2(-2cos(1\u03c0x - 1) + 1) - 2))^2 + 2((-3(-2cos(1\u03c0x - 1) + 1) + 3)/(-2(-2cos(1\u03c0x - 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2((3(2sin(3\u03c0x - 1)) + 1)/(3(2sin(3\u03c0x - 1)) - 2)) - 5 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) = -2(-3x^2 + 1x + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3|(2e^(2x) - 3) - 2| - 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(3x^2 + 3x + 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1111", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-2cos(3\u03c0x)) + 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(3sin(3\u03c0x + 3) + 3)^2 + 1(3sin(3\u03c0x + 3) + 3) + 2 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 -2((-1(-1|(-3x^2 + 4x + 3) + 3| + 1) + 2)/(-1(-1|(-3x^2 + 4x + 3) + 3| + 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) = (-1(1sin(3\u03c0x - 2) + 2) + 2)/(-1(1sin(3\u03c0x - 2) + 2) + 3) 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) = 1((2x - 2)/(3x - 1))^2 - 2((2x - 2)/(3x - 1)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(2\u03c0((1(-4(3x - 5)^2 + 4))/(-2(-4(3x - 5)^2 + 4) - 2)) - 3) - 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"}
{"messages": [{"content": "How many zeros does the function f(x) = 1sin(2\u03c0(3((-1x)/(-1x + 2))^2 + 5((-1x)/(-1x + 2)) - 1) + 2) 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) = -2cos(2\u03c0(-2x^2 - 5x - 3) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "794", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(2sin(1\u03c0(2|((2x)/(3x + 2)) + 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": "17", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(1x^2 - 5x - 4) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-1(-2(5x^2 + 1x - 5) - 1) - 3)/(1(-2(5x^2 + 1x - 5) - 1) + 2)) - 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) = (-2(-2|x - 3| + 2) - 1)/(3(-2|x - 3| + 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3(-1|x|) + 3) + 2)/(-1(3(-1|x|) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5((-2(1|(-5x^2 + 5x + 5)| - 3) + 1)/(-1(1|(-5x^2 + 5x + 5)| - 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) = 1cos(2\u03c0(1|(2x - 4) - 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 zeros does the function f(x) = (3(5(2|x - 3| - 1) - 3) - 2)/(3(5(2|x - 3| - 1) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(5x^2 + 3x - 4) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(4((3x - 2)/(3x)) - 4)^2 - 2(4((3x - 2)/(3x)) - 4) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(5(-1|x|) - 1) + 3) - 2 have in the interval [-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) = 3cos(2\u03c0(-3|(1(1x^2 - 5x) - 4)| - 3) - 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1039", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(3|(4(4x - 2)^2 - 4(4x - 2) + 3) - 2| - 3) + 1)/(-1(3|(4(4x - 2)^2 - 4(4x - 2) + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3|x - 2| - 1)^2 - 2(3|x - 2| - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(3\u03c0(3x^2 - 4x - 3) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "759", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((-2x + 2)/(1x - 3))^2 + 2((-2x + 2)/(1x - 3)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(4x + 4)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(3e^(1(-1((-1x + 3)/(-1x + 2))^2 + 2((-1x + 3)/(-1x + 2)) + 1)) - 3) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-3sin(3\u03c0((-2x + 2)/(-3x + 4)) + 3) + 3) + 1 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": "How many solutions does the equation (3(-5x^2 - 2x + 5) + 1)/(3(-5x^2 - 2x + 5) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(-5x^2 + 4x - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1001", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(2((-1x)/(2x - 1)) + 1)| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0(4(-2|(1x^2 + 3) - 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": "1316", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-1|(3x - 5) - 2| - 1) + 3)/(-1(-1|(3x - 5) - 2| - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1|(-4((-2x - 2)/(-2x - 1))^2) + 2| - 2) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((-3(2|x| - 1))/(-3(2|x| - 1) - 2)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(2|(-3sin(3\u03c0x + 2) - 1) - 1| - 2)^2 - 5 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) = -2cos(2\u03c0(2(1|((1x - 1)/(2x + 1))| + 1)^2 + 1(1|((1x - 1)/(2x + 1))| + 1) + 2) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(-2e^(1(2|x - 3| - 1)) + 2)^2 + 4(-2e^(1(2|x - 3| - 1)) + 2) - 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) = (-3(3(5x - 2)^2 - 5(5x - 2)) - 3)/(-1(3(5x - 2)^2 - 5(5x - 2)) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(4(-1(-3|x|) - 1)^2 + 1(-1(-3|x|) - 1)) + 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1040", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(2(2e^(1((2x)/(-1x + 3))) - 3)^2 + 5(2e^(1((2x)/(-1x + 3))) - 3) - 1) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(5(2|x - 2| - 1)^2 + 4(2|x - 2| - 1) - 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) = 3sin(1\u03c0(3x + 1) - 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 solutions does the equation 3(-3x^2 + 1x + 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((-3x - 3)/(-1x - 1)) - 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(3sin(3\u03c0((-1x)/(2x + 3)) + 3) + 2) - 4 = 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 zeros does the function f(x) = (1(3x^2 - 4x - 3) + 2)/(-3(3x^2 - 4x - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-2|x| + 1) - 2)/(1(-2|x| + 1)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(1\u03c0((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": "44", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2((1(2|(2sin(2\u03c0x + 2)) - 3| - 3) - 2)/(2(2|(2sin(2\u03c0x + 2)) - 3| - 3) + 3))^2 - 3((1(2|(2sin(2\u03c0x + 2)) - 3| - 3) - 2)/(2(2|(2sin(2\u03c0x + 2)) - 3| - 3) + 3)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0((1(5x - 4))/(3(5x - 4) + 3)) - 1) - 2 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 zeros does the function f(x) = -4(5(-1cos(3\u03c0(3|x - 1| - 2) + 1) - 1)^2 + 5(-1cos(3\u03c0(3|x - 1| - 2) + 1) - 1) - 5) - 1 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": "Determine the number of values x in [-10, 10] where f(x) = -1(-3e^(2(3|((3x - 2)/(1x))|)) + 1)^2 - 3(-3e^(2(3|((3x - 2)/(1x))|)) + 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(2\u03c0((1(5x - 2) - 1)/(1(5x - 2) + 1)) - 2) + 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": "How many zeros does the function f(x) = 3sin(1\u03c0(2|(-4x^2 - 4x + 3) - 3|) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1207", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((3(5(3cos(2\u03c0x + 3) + 2) + 2) - 3)/(1(5(3cos(2\u03c0x + 3) + 2) + 2) - 3))^2 + 3((3(5(3cos(2\u03c0x + 3) + 2) + 2) - 3)/(1(5(3cos(2\u03c0x + 3) + 2) + 2) - 3)) - 3 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((-1x + 2)/(-2x - 2))^2 + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-1(3sin(1\u03c0(3|x - 2| - 3) + 3) + 3) + 1)/(-1(3sin(1\u03c0(3|x - 2| - 3) + 3) + 3) + 2)) + 3 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(-1|(2sin(2\u03c0x - 3) + 1) - 1|) - 1)/(1(-1|(2sin(2\u03c0x - 3) + 1) - 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(2|x + 2| - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-2sin(2\u03c0x + 3)) + 1)/(1(-2sin(2\u03c0x + 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": "Find the number of x-intercepts of the function f(x) = 3(-1|((-1x + 1)/(2x - 3))| + 1)^2 + 3(-1|((-1x + 1)/(2x - 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 -3|((-1(2(-4x^2 - 5x - 1) + 1) + 2)/(-3(2(-4x^2 - 5x - 1) + 1) - 1)) - 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3((-1(-3|x - 2| + 1) + 2)/(-3(-3|x - 2| + 1) + 1))^2 + 2((-1(-3|x - 2| + 1) + 2)/(-3(-3|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": "How many solutions does the equation (1(1|(-1x^2 + 1x + 5) - 2| - 1) - 2)/(2(1|(-1x^2 + 1x + 5) - 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 solutions does the equation -1cos(1\u03c0((-2(-2(4x + 4)^2 + 2) + 1)/(-1(-2(4x + 4)^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": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1|((3x - 3)/(-2x)) + 2| - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(-2((3(2x^2 + 5x - 4) + 2)/(2(2x^2 + 5x - 4) + 3)) + 4) + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((-2(-2|(-1x^2 + 5x) + 3| + 1) - 2)/(-1(-2|(-1x^2 + 5x) + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(5x - 3) - 2) + 2 equals zero.\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) = -2sin(3\u03c0(-4x + 2) + 1) + 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": "How many zeros does the function f(x) = 5(3|(4x + 5) + 3| - 3)^2 - 3(3|(4x + 5) + 3| - 3) - 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": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(-2|x + 1| + 1) + 1) - 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) = 2sin(1\u03c0(-1x + 2) - 3) + 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 -3((2(2x^2 + 2x - 5) + 1)/(-3(2x^2 + 2x - 5))) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-2(-3|(-5x - 1) - 2| + 3) - 3)/(-3(-3|(-5x - 1) - 2| + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-2e^(-1(-1x - 3)) + 1)^2 + 4(-2e^(-1(-1x - 3)) + 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(4((-1x + 3)/(1x))^2 + 1((-1x + 3)/(1x)) - 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) = -2|(-1sin(2\u03c0(-3x^2 + 4x + 1) + 2) + 1)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1168", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(2\u03c0(-1|((-3(-2x + 2) + 1)/(-2(-2x + 2) + 3)) - 2| - 3) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0((-3x + 1)/(-3x - 2)) - 3) + 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 zeros does the function f(x) = -1((1(-1|x + 2| + 3) - 3)/(2(-1|x + 2| + 3)))^2 - 1((1(-1|x + 2| + 3) - 3)/(2(-1|x + 2| + 3))) + 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": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0(1x) - 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 zeros does the function f(x) = (-2(-4(-2e^(1x) + 2)^2 - 3(-2e^(1x) + 2) + 4) + 3)/(-1(-4(-2e^(1x) + 2)^2 - 3(-2e^(1x) + 2) + 4) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1((2(-1x^2 - 5x + 4) - 1)/(-1(-1x^2 - 5x + 4) + 2)) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(4(1|x - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(3\u03c0(3|(1x^2 + 2x) + 3| - 1) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "756", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(3|(1sin(3\u03c0(5x) - 3) + 1) - 2|)^2 + 1(3|(1sin(3\u03c0(5x) - 3) + 1) - 2|) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(1|(-2(-2sin(1\u03c0x - 1) - 1)^2 + 2) + 3|) + 4 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) = -2(1(2sin(2\u03c0(1|x + 1| + 1)))^2 + 4(2sin(2\u03c0(1|x + 1| + 1))) + 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 -2sin(3\u03c0((-2x - 1)/(-1x + 2))) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "126", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2x + 2)^2 - 3(2x + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-3x^2 - 4x + 3) - 2)/(-2(-3x^2 - 4x + 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3|x - 3| - 2)^2 - 3(3|x - 3| - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-2cos(3\u03c0(1|x - 2| - 1) - 3) - 3)^2 - 5 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|(4(-1((-2x + 2)/(-2x - 3))^2 + 3((-2x + 2)/(-2x - 3)) - 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 zeros does the function f(x) = -1(1(-1|((-1x)/(3x + 2)) - 1| + 1) + 2)^2 - 4(1(-1|((-1x)/(3x + 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) = 1sin(1\u03c0(1(-5((-2x + 2)/(-3x - 3)) + 2)^2 - 3(-5((-2x + 2)/(-3x - 3)) + 2) - 5) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "255", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1|(-4((3x - 1)/(3x - 2)) - 3) + 1| + 2)^2 - 1(-1|(-4((3x - 1)/(3x - 2)) - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2((3(-3(-3|x - 2| + 2)^2 - 5(-3|x - 2| + 2)))/(1(-3(-3|x - 2| + 2)^2 - 5(-3|x - 2| + 2)) + 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 -2cos(3\u03c0(-2|(1((-3x + 2)/(1x - 3)) + 4) - 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": "133", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(-1x + 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": "Find the number of x-intercepts of the function f(x) = 5(-2sin(1\u03c0(-3x^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": "600", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(3sin(1\u03c0x + 2)) - 3| - 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": "How many zeros does the function f(x) = -3(3|((3(2x^2 - 5x + 2) + 2)/(-1(2x^2 - 5x + 2) + 2)) - 1| - 3) - 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) = -1(2|x - 3| + 2)^2 + 5(2|x - 3| + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3sin(1\u03c0x - 2) + 1) - 2)/(-3(3sin(1\u03c0x - 2) + 1) + 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) = 2cos(2\u03c0(-3|x + 2| - 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": "Find the number of x-intercepts of the function f(x) = 2sin(3\u03c0(-1|(-4(1x^2 - 1x + 4) + 3) + 2| - 1) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "944", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1(5x^2 - 2x - 1) + 2) + 3| - 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 (-1(-4(-3|(-3x - 1) + 1| + 1)^2 - 2(-3|(-3x - 1) + 1| + 1) - 1) - 3)/(-1(-4(-3|(-3x - 1) + 1| + 1)^2 - 2(-3|(-3x - 1) + 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) = -1|(-4(4x^2 + 3x - 1) + 5) - 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 solutions does the equation (3(3cos(3\u03c0x - 2) - 2))/(-3(3cos(3\u03c0x - 2) - 2) + 4) = 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 solutions does the equation (3(-4(1(-1|x + 2| - 3) + 3)^2 - 1(1(-1|x + 2| - 3) + 3) + 2) - 3)/(1(-4(1(-1|x + 2| - 3) + 3)^2 - 1(1(-1|x + 2| - 3) + 3) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-3|(-1cos(2\u03c0((-3x - 1)/(2x)) - 3) - 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": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2|(5((2x - 3)/(3x - 2)) - 1) - 1| + 3)^2 - 5(-2|(5((2x - 3)/(3x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(1(1|((-1x + 1)/(2x - 1)) + 2| - 3)^2 + 3(1|((-1x + 1)/(2x - 1)) + 2| - 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": "33", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(-3|x + 3|) + 3) - 1 have in the interval [-10, 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 3cos(1\u03c0(3x + 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": "How many zeros does the function f(x) = 3(1(2cos(1\u03c0x + 1) - 3)^2 + 1(2cos(1\u03c0x + 1) - 3) - 5) + 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(2sin(1\u03c0x - 2)) + 2)/(1(2sin(1\u03c0x - 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": "How many zeros does the function f(x) = 2|(-1((2x + 2)/(3x + 1)) + 5) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-2x^2 - 3x))/(-3(-2x^2 - 3x) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(3((-1(-1x + 3) + 1)/(2(-1x + 3) - 1))^2 + 2((-1(-1x + 3) + 1)/(2(-1x + 3) - 1)) - 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": "How many zeros does the function f(x) = 5(1|((-3(3e^(-2x) - 1) - 3)/(3(3e^(-2x) - 1) - 2)) + 2| - 2)^2 + 2(1|((-3(3e^(-2x) - 1) - 3)/(3(3e^(-2x) - 1) - 2)) + 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": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0((-3(4x) + 3)/(2(4x) - 1))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-1(-1(-3|x - 2|))^2 + 3(-1(-3|x - 2|)) + 3) - 3)/(-3(-1(-1(-3|x - 2|))^2 + 3(-1(-3|x - 2|)) + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(4x + 3)| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(4x + 4) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(1e^(-2((1(-5x^2 + 2x) + 1)/(3(-5x^2 + 2x) - 1))) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(2(-2((-1x)/(1x + 3)) + 3)^2 - 1(-2((-1x)/(1x + 3)) + 3) - 5) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-2(5(-3sin(3\u03c0x - 1) - 3)^2 - 3) + 3) - 3)/(-3(-2(5(-3sin(3\u03c0x - 1) - 3)^2 - 3) + 3) + 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) = 3(2((3x - 1)/(-2x + 1))^2 - 4((3x - 1)/(-2x + 1)) - 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-1sin(1\u03c0(-5((1x)/(-1x - 1))^2 + 4((1x)/(-1x - 1)) + 2) + 3) + 2) - 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "117", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-1(-2|x - 2| + 2)^2 + 5(-2|x - 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": "741", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-4(2|x + 3| - 3) + 4)^2 - 3(-4(2|x + 3| - 3) + 4) - 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((-2x - 3)/(-1x - 2))^2 - 1((-2x - 3)/(-1x - 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(4(2|x + 1| - 1) + 2) + 3)/(-1(4(2|x + 1| - 1) + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-3|(4x^2 + 5x - 1) + 3| + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((-2(3(1x + 2)^2 + 3(1x + 2) - 5) + 3)/(-1(3(1x + 2)^2 + 3(1x + 2) - 5) + 3)) - 1) + 2 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": "Determine the number of values x in [-10, 10] where f(x) = -1|(2(1((3x)/(3x + 3))^2 - 2) + 4)| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(1(-2sin(1\u03c0(4x + 4) - 1) + 1)^2 + 5(-2sin(1\u03c0(4x + 4) - 1) + 1) - 5) + 2)/(-1(1(-2sin(1\u03c0(4x + 4) - 1) + 1)^2 + 5(-2sin(1\u03c0(4x + 4) - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(5x - 5) - 3| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-2sin(1\u03c0(3|(-4x^2 - 2x - 5)| - 1) - 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "971", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3e^(2(-2((1(-1|x - 1| - 1) - 3)/(1(-1|x - 1| - 1)))^2 - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-2cos(3\u03c0x - 1) + 1)^2 - 3(-2cos(3\u03c0x - 1) + 1) = 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 -5((2(2x^2 + 1))/(3(2x^2 + 1) - 2)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(2sin(2\u03c0x + 3) + 1) + 1)/(-1(2sin(2\u03c0x + 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": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0((-2(-4(1|x| + 1)^2 + 1(1|x| + 1) + 1) + 3)/(1(-4(1|x| + 1)^2 + 1(1|x| + 1) + 1) + 3)) + 3) - 1 equals zero.\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) = 1(-2(-2|((3x - 3)/(-2x - 2)) + 2| + 2) - 4)^2 + 4(-2(-2|((3x - 3)/(-2x - 2)) + 2| + 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 zeros does the function f(x) = 3(2sin(2\u03c0x - 2) + 3) - 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) = (2(2sin(2\u03c0x + 3) - 2) + 1)/(-1(2sin(2\u03c0x + 3) - 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": "Determine the number of values x in [-10, 10] where f(x) = 3|(1(4x + 1)^2 + 1(4x + 1) - 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 zeros does the function f(x) = 5(1e^(1(1x + 5)) - 3)^2 - 2(1e^(1(1x + 5)) - 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(1\u03c0(2x + 5) + 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": "How many solutions does the equation 5(2x^2 + 1x - 5) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(2|((2x - 3)/(-1x - 3)) - 3| - 3) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3(-2cos(2\u03c0(3|x| - 2) + 2) - 1) - 4) + 2)/(2(3(-2cos(2\u03c0(3|x| - 2) + 2) - 1) - 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) = (3(-1(1x^2 - 3x - 3) + 1) - 1)/(-1(-1(1x^2 - 3x - 3) + 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0((2(-3|x + 3| + 2) - 1)/(1(-3|x + 3| + 2)))) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(2sin(2\u03c0x - 1) - 2)^2 - 5(2sin(2\u03c0x - 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": "Determine the number of values x in [-10, 10] where f(x) = -1(-1sin(1\u03c0x - 1) + 3)^2 + 4(-1sin(1\u03c0x - 1) + 3) - 4 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|(2((2x + 1)/(1x)) - 1) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(3x - 3)^2 + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0((-2x - 3)/(-3x + 2)) + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(1x^2 + 3x + 3) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "410", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((-1(1cos(1\u03c0x + 3) + 1) + 1)/(-3(1cos(1\u03c0x + 3) + 1))) - 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) = -2|(-1cos(2\u03c0(4x^2 - 4x - 4) - 3)) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1310", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(3cos(3\u03c0(1((2x + 1)/(-3x + 4)) - 4) + 3) - 1)| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0((-2(-5x^2 - 1) - 1)/(-3(-5x^2 - 1) + 2))) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-1x^2 + 2x + 3) + 2)/(2(-1x^2 + 2x + 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((-3x - 3)/(1x - 3))^2 + 4((-3x - 3)/(1x - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2e^(1(-3|x - 3| + 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-2e^(2(2|x + 3| - 1)) + 3) + 3)/(2(-2e^(2(2|x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-2|x - 1| - 1)^2 + 4(-2|x - 1| - 1) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(1\u03c0(-3x^2 - 3x + 4) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "278", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-2|(3e^(1x) - 2) - 3| + 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": "Determine the number of values x in [-10, 10] where f(x) = (-2(-5(5x - 1)^2 + 2(5x - 1)) - 3)/(-2(-5(5x - 1)^2 + 2(5x - 1)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-3|x + 1| + 3) - 3)/(2(-3|x + 1| + 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1|(-1(3x^2 + 1x + 2) + 2) + 3| - 2) + 1)/(2(1|(-1(3x^2 + 1x + 2) + 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": "Find the number of x-intercepts of the function f(x) = -2|(3sin(1\u03c0(-1x + 1) - 1) - 3)| + 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": "Determine the number of values x in [-10, 10] where f(x) = 3(-4x)^2 + 1(-4x) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((-2(4x - 4))/(2(4x - 4) + 3)) - 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-5x^2 - 2x + 2) - 2)/(2(-5x^2 - 2x + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(1cos(1\u03c0(-5x^2 + 5x) + 3) + 2) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2|(-2e^(1(1x^2 + 3x - 3))) + 3| - 3) - 3)/(3(2|(-2e^(1(1x^2 + 3x - 3))) + 3| - 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) = (2(4(-4x^2 + 4x + 1) - 1) - 3)/(2(4(-4x^2 + 4x + 1) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-1sin(1\u03c0(-4(-2|x + 1| + 2) - 3) - 1) + 1))/(-3(-1sin(1\u03c0(-4(-2|x + 1| + 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": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2cos(2\u03c0(-1|x + 3| + 1) + 1) - 1) - 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(1(1|(-3x^2 - 2x - 2) + 2| - 3)))/(-3(1(1|(-3x^2 - 2x - 2) + 2| - 3)) + 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(2(-4x^2 + 1x + 2) + 5) - 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|((1(5x - 5) - 2)/(-3(5x - 5) - 3)) + 1| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3(1|x| - 1)^2 + 2(1|x| - 1) - 5) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1cos(3\u03c0(-1|(-4x^2 - 4x) - 1|) + 3) - 2) - 3)/(-3(1cos(3\u03c0(-1|(-4x^2 - 4x) - 1|) + 3) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1034", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1|(1((1x)/(-1x + 3))^2 + 2((1x)/(-1x + 3)) - 3) + 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|(4(-3sin(3\u03c0x + 3)) - 3) - 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": "How many zeros does the function f(x) = 3(3x^2 - 5) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-1(3(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) + 4) + 1) + 3)/(-1(-1(3(2|x - 1| - 3)^2 + 5(2|x - 1| - 3) + 4) + 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) = -1(1x^2 + 4x + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2cos(2\u03c0(2x^2 - 2x))) + 2)/(1(2cos(2\u03c0(2x^2 - 2x))) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-2|(-1(3x^2 - 4) - 5) + 1| + 3) - 3)/(-1(-2|(-1(3x^2 - 4) - 5) + 1| + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0(-4(2|x| + 1)^2 - 1(2|x| + 1) - 5) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1201", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((2(1sin(2\u03c0x - 2) - 1) + 2)/(1(1sin(2\u03c0x - 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": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(-5x^2 + 3x - 3) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1424", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((3(2cos(3\u03c0x + 3) - 1) - 3)/(-2(2cos(3\u03c0x + 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2e^(1(-4((-3x + 3)/(-3x + 4))^2 + 1((-3x + 3)/(-3x + 4)) + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1cos(1\u03c0(-2(1|x + 3| + 3) + 4)) - 1 = 0 have in the range [-10, 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) = (-2(1(-2|(4x + 4) - 3| + 2)^2 - 5(-2|(4x + 4) - 3| + 2) + 3) - 2)/(-2(1(-2|(4x + 4) - 3| + 2)^2 - 5(-2|(4x + 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": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-2|(-3x^2 - 2x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(2\u03c0(-2(-1|x + 1| + 3)^2 - 4(-1|x + 1| + 3) + 4) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "424", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(4(-2x^2 - 2x - 2) + 5) + 3)/(1(4(-2x^2 - 2x - 2) + 5) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2x + 2)^2 + 5(2x + 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((2(1x^2 + 3x + 3) - 2)/(-1(1x^2 + 3x + 3) + 2)) + 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(2\u03c0(-3(-5((-2x + 2)/(1x - 3)) + 2)^2 - 3(-5((-2x + 2)/(1x - 3)) + 2) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1306", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1sin(2\u03c0(2(-1|x - 3| + 1) - 1) + 2) + 1)^2 + 5(1sin(2\u03c0(2(-1|x - 3| + 1) - 1) + 2) + 1) - 5 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|((2x - 2)/(2x - 3)) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((-1(3|(-1x - 1) + 1| - 1))/(-1(3|(-1x - 1) + 1| - 1) + 2))^2 - 3((-1(3|(-1x - 1) + 1| - 1))/(-1(3|(-1x - 1) + 1| - 1) + 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-4((3(-1x^2 - 1x + 4) + 3)/(1(-1x^2 - 1x + 4) + 2)) + 2) - 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 1|((-1(-1(4x + 1)^2 + 5(4x + 1) + 2))/(-1(-1(4x + 1)^2 + 5(4x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(5(5(2|x + 1| - 3) + 2)^2 - 5(5(2|x + 1| - 3) + 2) - 4) + 2)/(1(5(5(2|x + 1| - 3) + 2)^2 - 5(5(2|x + 1| - 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": "Determine the number of values x in [-10, 10] where f(x) = 2|(-4(5x^2 + 4x - 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 zeros does the function f(x) = (3(-3sin(1\u03c0x + 3) + 1) - 2)/(-1(-3sin(1\u03c0x + 3) + 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2(1|((1x - 3)/(-1x + 2)) - 3| - 3)^2 - 2(1|((1x - 3)/(-1x + 2)) - 3| - 3) + 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 zeros does the function f(x) = (-1(-3x^2 - 1x))/(-1(-3x^2 - 1x) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1|x - 2| + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((-2x + 3)/(-2x))^2 - 3((-2x + 3)/(-2x)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-5x^2 - 5x - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(1x^2 - 4x - 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 zeros does the function f(x) = -5((-2(5(1|x - 2| - 2) - 1) + 1)/(3(5(1|x - 2| - 2) - 1) - 1))^2 + 1((-2(5(1|x - 2| - 2) - 1) + 1)/(3(5(1|x - 2| - 2) - 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) = -1(-3cos(2\u03c0((-3x + 1)/(-1x + 2)) - 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "105", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-1|x + 2| + 3)^2 - 1(-1|x + 2| + 3) + 5 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(1\u03c0((-1(1x) - 1)/(1(1x)))) + 2 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) = -2(-2cos(2\u03c0(-2x - 1) + 3) + 2)^2 - 4(-2cos(2\u03c0(-2x - 1) + 3) + 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": "Determine the number of values x in [-10, 10] where f(x) = -4((-2(4x^2 + 3x - 5) + 3)/(-2(4x^2 + 3x - 5) - 3)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(3cos(2\u03c0x + 1) - 2)^2 + 5(3cos(2\u03c0x + 1) - 2) - 5 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) = (-1(3(2|(1cos(1\u03c0x + 2) + 3) - 2| - 3) - 3) - 3)/(2(3(2|(1cos(1\u03c0x + 2) + 3) - 2| - 3) - 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(1sin(1\u03c0(1x^2 + 4x + 1) - 3)) - 1| + 3 equals zero.\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) = -1(3cos(1\u03c0((-3x + 3)/(-3x - 3)) + 3) + 3)^2 - 3(3cos(1\u03c0((-3x + 3)/(-3x - 3)) + 3) + 3) + 5 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 solutions does the equation (-2(4(-1sin(2\u03c0(-1|x + 2| - 2) + 1) + 1)^2 + 2(-1sin(2\u03c0(-1|x + 2| - 2) + 1) + 1) - 5) + 1)/(1(4(-1sin(2\u03c0(-1|x + 2| - 2) + 1) + 1)^2 + 2(-1sin(2\u03c0(-1|x + 2| - 2) + 1) + 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": "Find the number of x-intercepts of the function f(x) = (-1(-1x^2 + 5x - 4) - 1)/(-3(-1x^2 + 5x - 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-1((2x - 1)/(-1x - 3)) + 3) - 2) + 2 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": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(-2|(3((1x - 1)/(-2x - 1)) + 3) + 2| - 2) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(5x^2 + 2x - 5) - 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) = -1cos(3\u03c0(3|((-3x + 1)/(-2x + 3)) + 3| + 1) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3cos(3\u03c0x) + 1) - 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) = -2cos(2\u03c0(-1(2|(-3x + 4)| - 1)^2 - 2(2|(-3x + 4)| - 1) + 4) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1133", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(1|(-1((1x + 3)/(1x)))| - 3) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "107", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-2cos(3\u03c0x - 1)) + 1| - 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|(-4(-1((2x + 1)/(1x + 3)) - 3)^2 - 3(-1((2x + 1)/(1x + 3)) - 3) + 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": "How many solutions does the equation 2|((2x)/(-2x + 3))| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1e^(2(-2(-4x)^2 - 4(-4x) + 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-2cos(2\u03c0x - 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": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(4x^2 - 5x) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-3cos(2\u03c0x - 2) + 3) + 3)/(-3(-3cos(2\u03c0x - 2) + 3) - 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|((3x - 3)/(-1x + 3)) - 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-2|(-4(-1x - 2)^2 - 2(-1x - 2) + 5)| + 2) - 3)/(-3(-2|(-4(-1x - 2)^2 - 2(-1x - 2) + 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 (-1(1(1|(2x + 1) - 1| - 1)^2 - 2(1|(2x + 1) - 1| - 1) - 1) - 1)/(-2(1(1|(2x + 1) - 1| - 1)^2 - 2(1|(2x + 1) - 1| - 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": "Determine the number of values x in [-10, 10] where f(x) = (-1(-1|(1x^2 - 5x + 2) - 2| + 1) - 2)/(1(-1|(1x^2 - 5x + 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) = (-1(1(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) - 2) + 1)/(-2(1(1|x - 3| - 2)^2 + 5(1|x - 3| - 2) - 2) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3e^(-1(-1(-3|x - 1| - 1)^2 - 5(-3|x - 1| - 1) - 5)) - 3) - 3)/(1(3e^(-1(-1(-3|x - 1| - 1)^2 - 5(-3|x - 1| - 1) - 5)) - 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(-2|(-5x^2 - 1x + 2) + 3| + 2) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "982", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(3\u03c0(3((-1(1x - 5) - 3)/(-3(1x - 5) + 2))^2 + 4((-1(1x - 5) - 3)/(-3(1x - 5) + 2)) - 4) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(1(-3(-1|((1x - 3)/(2x)) - 1|)^2 - 3(-1|((1x - 3)/(2x)) - 1|) + 4)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-2(-1|x|)^2 + 2) - 1)/(-1(-2(-1|x|)^2 + 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-5(3cos(3\u03c0(-2x + 4) - 1))^2 + 1(3cos(3\u03c0(-2x + 4) - 1)) + 3))/(-2(-5(3cos(3\u03c0(-2x + 4) - 1))^2 + 1(3cos(3\u03c0(-2x + 4) - 1)) + 3) + 3) 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": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1cos(3\u03c0x - 1) + 1))/(1(-1cos(3\u03c0x - 1) + 1) - 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) = 3e^(-1(1(-1|((1x + 2)/(3x + 1)) + 3| + 1)^2 + 2(-1|((1x + 2)/(3x + 1)) + 3| + 1) - 5)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(1x^2 - 5x + 4) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(1(2|x - 2| + 3)^2 - 2(2|x - 2| + 3) - 5) - 2)/(1(1(2|x - 2| + 3)^2 - 2(2|x - 2| + 3) - 5) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|((-1x + 3)/(-1x - 2)) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((3(2x^2 + 5x + 1) + 2)/(-3(2x^2 + 5x + 1))) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-4(-4(-3|x + 3| + 2)^2 + 4(-3|x + 3| + 2)) - 4) - 1)/(-2(-4(-4(-3|x + 3| + 2)^2 + 4(-3|x + 3| + 2)) - 4) - 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(-2|(2e^(-1x) - 3) - 2| + 3) - 3)/(1(-2|(2e^(-1x) - 3) - 2| + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1e^(1(1|(-1x^2 + 5x + 5) - 2| - 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 (1(3(-1|x| + 2) - 1) - 1)/(-3(3(-1|x| + 2) - 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1|((2(4x - 3) + 1)/(2(4x - 3))) - 2|)^2 - 5(-1|((2(4x - 3) + 1)/(2(4x - 3))) - 2|) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-1cos(2\u03c0(-2|(3x + 2) + 3| - 1) - 2) - 2) + 1)/(-1(-1cos(2\u03c0(-2|(3x + 2) + 3| - 1) - 2) - 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4((1(-4(3|x - 1| - 1) + 3) - 3)/(-1(-4(3|x - 1| - 1) + 3) + 2))^2 - 4((1(-4(3|x - 1| - 1) + 3) - 3)/(-1(-4(3|x - 1| - 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(3cos(1\u03c0(3(-1|x + 2| + 1)^2 + 2(-1|x + 2| + 1) - 5) + 1) - 3) + 3)/(-1(3cos(1\u03c0(3(-1|x + 2| + 1)^2 + 2(-1|x + 2| + 1) - 5) + 1) - 3) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "484", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(3|((-1x + 3)/(3x + 3)) - 1| - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-1|(5((-2x + 3)/(2x + 1))) - 2| + 3)^2 - 4(-1|(5((-2x + 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": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(1(1|x| + 2) - 1) - 3)/(2(1(1|x| + 2) - 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2(2sin(1\u03c0x + 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": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-3sin(3\u03c0(1|((-1x - 3)/(3x)) - 1| + 3) - 1) + 1)^2 + 1(-3sin(3\u03c0(1|((-1x - 3)/(3x)) - 1| + 3) - 1) + 1) + 3 where -10 \u2264 x \u2264 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 (2(2|(4x + 5) + 1|) - 3)/(3(2|(4x + 5) + 1|) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-2|(1x - 2)| + 3)^2 + 1(-2|(1x - 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": "Find the number of x-intercepts of the function f(x) = -1|(-1(-1((-3x + 3)/(-2x - 1))^2 + 2((-3x + 3)/(-2x - 1)) + 3) + 5) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-1(-4(-1|x| - 1)^2 - 5(-1|x| - 1) + 4) - 1) + 2)/(-2(-1(-4(-1|x| - 1)^2 - 5(-1|x| - 1) + 4) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(3|((-3(-3x^2 + 5x - 4) - 2)/(3(-3x^2 + 5x - 4) - 2)) + 3| - 1) + 1) + 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) = 3(-1((2x + 2)/(1x + 3)) - 2)^2 + 3(-1((2x + 2)/(1x + 3)) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-2cos(2\u03c0x + 1) + 2)^2 - 1(-2cos(2\u03c0x + 1) + 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 5((2(-1x - 3) + 3)/(1(-1x - 3)))^2 - 2((2(-1x - 3) + 3)/(1(-1x - 3))) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(3cos(2\u03c0x + 2) - 2) + 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": "How many zeros does the function f(x) = -1e^(-2(5x^2 - 5x - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(4((2(1|x + 1| - 2))/(2(1|x + 1| - 2) - 1))^2 - 2((2(1|x + 1| - 2))/(2(1|x + 1| - 2) - 1)) - 5) + 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) = (-2(-2cos(2\u03c0(-3x^2 + 3x) - 2) + 1) - 1)/(-3(-2cos(2\u03c0(-3x^2 + 3x) - 2) + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "238", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((-3x - 3)/(-2x + 3))^2 + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-2cos(1\u03c0(5((-3x)/(-1x + 2)) + 5)) + 1)^2 + 4(-2cos(1\u03c0(5((-3x)/(-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": "238", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-2cos(3\u03c0x - 1) - 1) + 3)/(2(-2cos(3\u03c0x - 1) - 1) - 3) 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) = -1(-2x + 4)^2 - 1(-2x + 4) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(-1((2x)/(2x + 2))^2 + 4((2x)/(2x + 2)) - 1) - 2) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3cos(1\u03c0(2(-2x^2 - 2x - 3) - 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "364", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-4x^2 + 3x + 1) - 2)/(-2(-4x^2 + 3x + 1) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1((-2x + 3)/(3x - 2))^2 + 4((-2x + 3)/(3x - 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-1|(4x^2 - 5x - 2)| + 2))/(1(-1|(4x^2 - 5x - 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) = -3(-1x + 1)^2 + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(3cos(3\u03c0(2(-1|x - 2| - 3)) + 1) - 2) - 2)/(-3(3cos(3\u03c0(2(-1|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": "60", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-5(1x + 4)^2 - 3(1x + 4) + 3) - 2)/(1(-5(1x + 4)^2 - 3(1x + 4) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-1(-3sin(2\u03c0((2x - 1)/(-1x + 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": "72", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-2((3x - 3)/(2x - 1))^2 - 1((3x - 3)/(2x - 1))) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-2(-3|x + 3| - 1)^2 - 4(-3|x + 3| - 1) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(5((-1x - 2)/(1x + 1))) - 1| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2e^(-1(-1|x - 1| + 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4((-2(-2sin(3\u03c0(-2x - 4) + 1) - 3) - 3)/(2(-2sin(3\u03c0(-2x - 4) + 1) - 3) + 1))^2 - 2((-2(-2sin(3\u03c0(-2x - 4) + 1) - 3) - 3)/(2(-2sin(3\u03c0(-2x - 4) + 1) - 3) + 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|(1x^2 + 1x - 1) - 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 solutions does the equation -3cos(2\u03c0((-2(1x^2 + 5x - 3) + 2)/(-3(1x^2 + 5x - 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": "11", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1((-3x + 3)/(1x - 3))^2 + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-2sin(3\u03c0(-2|(5x - 2) - 2| - 1) + 3) - 1) - 3)/(-1(-2sin(3\u03c0(-2|(5x - 2) - 2| - 1) + 3) - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-3sin(3\u03c0((3(1x - 2) - 3)/(-1(1x - 2) + 2)) - 1) - 2) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-3(-2|(2x^2 + 3x + 2) - 3| + 2) - 4))/(-2(-3(-2|(2x^2 + 3x + 2) - 3| + 2) - 4) - 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(-5x^2 + 4) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((-2(1(-4x - 5)^2 - 1(-4x - 5) + 3))/(2(1(-4x - 5)^2 - 1(-4x - 5) + 3) - 3)) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-4(-2cos(2\u03c0(1x^2 + 2x - 3) + 1) + 2) + 4) - 3)/(-3(-4(-2cos(2\u03c0(1x^2 + 2x - 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": "145", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(4((3x - 1)/(-2x - 1))) - 2) + 2 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": "Find the number of x-intercepts of the function f(x) = 4(2((3x)/(1x - 3)) + 3)^2 - 4(2((3x)/(1x - 3)) + 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(1|(5(-4x^2 + 1x - 1) + 5) + 2| - 2))/(3(1|(5(-4x^2 + 1x - 1) + 5) + 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) = -2(-1|(2((-1x - 1)/(3x + 1)) + 4) + 2| + 1)^2 - 3(-1|(2((-1x - 1)/(3x + 1)) + 4) + 2| + 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3|(2cos(1\u03c0(5x^2 - 4x + 4) - 3)) - 1| - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1210", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0((1x - 3)/(-2x + 1)) + 1) - 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": "How many zeros does the function f(x) = 3((-3x - 2)/(3x - 2))^2 + 4((-3x - 2)/(3x - 2)) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(2sin(2\u03c0x)) - 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 zeros does the function f(x) = 5(-3sin(2\u03c0x + 1) + 2)^2 - 5(-3sin(2\u03c0x + 1) + 2) + 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) = (3(-3(2cos(3\u03c0x - 3)) + 4))/(-1(-3(2cos(3\u03c0x - 3)) + 4) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((1(-2|(-5x^2 - 3x - 1) + 1| + 3))/(-3(-2|(-5x^2 - 3x - 1) + 1| + 3) - 2)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(3|(4(3x^2 - 5) - 5)| - 2))/(-3(3|(4(3x^2 - 5) - 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": "How many solutions does the equation 4((1(-1e^(1(4x - 2)) + 3) - 1)/(-3(-1e^(1(4x - 2)) + 3) + 2))^2 + 5((1(-1e^(1(4x - 2)) + 3) - 1)/(-3(-1e^(1(4x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-2cos(3\u03c0x - 3) - 2) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(1\u03c0(-1|(5x^2 - 5x) + 1|) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "980", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(2x + 5)^2 + 4(2x + 5) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((3(1(3x)^2 + 5(3x) + 3) - 3)/(3(1(3x)^2 + 5(3x) + 3) + 3)) + 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(5x^2 + 5x + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0(-1|(-2((3x - 2)/(2x - 3)) + 5) - 3| + 1) - 1) 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": "Find the number of x-intercepts of the function f(x) = 1sin(3\u03c0(2x - 5) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2sin(3\u03c0(2x^2 + 5x - 4) - 1) + 3) - 2)/(2(2sin(3\u03c0(2x^2 + 5x - 4) - 1) + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1101", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-4((-1x + 3)/(1x))^2 + 3((-1x + 3)/(1x)) + 3) + 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(5(-3x + 4)^2 - 4(-3x + 4) - 1))/(-3(5(-3x + 4)^2 - 4(-3x + 4) - 1) + 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2((2(1(3|x| - 3) + 2) + 1)/(2(1(3|x| - 3) + 2) - 1))^2 - 3((2(1(3|x| - 3) + 2) + 1)/(2(1(3|x| - 3) + 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": "How many zeros does the function f(x) = 2cos(2\u03c0(-3|x| - 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": "Find the number of x-intercepts of the function f(x) = (-3(-2(-1|x + 1| - 1)^2 - 2(-1|x + 1| - 1) + 1))/(2(-2(-1|x + 1| - 1)^2 - 2(-1|x + 1| - 1) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(1(1((2x - 3)/(-3x + 4))^2 + 1((2x - 3)/(-3x + 4)) + 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": "How many zeros does the function f(x) = 4(1sin(2\u03c0x - 3) - 1)^2 + 2(1sin(2\u03c0x - 3) - 1) - 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 zeros does the function f(x) = -2(5x^2 - 3x - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-3((-2(3x + 1) - 2)/(-1(3x + 1) - 3))^2 + 2((-2(3x + 1) - 2)/(-1(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": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3x + 1)^2 - 3(3x + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((3(2(-1|x - 3| - 3)^2 + 5(-1|x - 3| - 3) - 4))/(2(2(-1|x - 3| - 3)^2 + 5(-1|x - 3| - 3) - 4) - 1)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-1x^2 + 5x + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(3cos(2\u03c0x + 1) + 2) + 1)/(3(3cos(2\u03c0x + 1) + 2) - 1) 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) = (2(-2(4x^2 - 4x - 5) - 1) + 3)/(1(-2(4x^2 - 4x - 5) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-1x^2 - 3x + 1) + 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-3cos(3\u03c0x - 3) + 3) - 2| + 3 = 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 -1|(-1sin(2\u03c0x - 1)) + 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": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-1|(4x) + 1| + 2) - 3) 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) = -5(3|x + 1| - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(2(2sin(2\u03c0x) + 2)^2 - 3(2sin(2\u03c0x) + 2) - 2))/(-1(2(2sin(2\u03c0x) + 2)^2 - 3(2sin(2\u03c0x) + 2) - 2) - 2) 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": "Find the number of x-intercepts of the function f(x) = -1cos(2\u03c0((1x + 2)/(3x - 2)) - 2) 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": "Find the number of x-intercepts of the function f(x) = (-3(1cos(3\u03c0x - 1)) + 3)/(2(1cos(3\u03c0x - 1)) + 1) 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": "How many zeros does the function f(x) = 3|((2(-5x^2 + 4x + 1) + 2)/(-2(-5x^2 + 4x + 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": "How many solutions does the equation 1sin(2\u03c0((2(-1x^2 - 3x - 1) - 1)/(3(-1x^2 - 3x - 1) - 2)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1(1|(2x^2 - 4x + 1) + 2| - 2) + 4) - 1)/(3(-1(1|(2x^2 - 4x + 1) + 2| - 2) + 4) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(3|((-1(-3x^2 + 5x + 3) + 2)/(1(-3x^2 + 5x + 3))) - 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": "101", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0((-1(-3(1x - 4)^2 + 3) + 2)/(3(-3(1x - 4)^2 + 3) - 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) = (-2(-1(-2|x - 2| - 1) - 4))/(1(-1(-2|x - 2| - 1) - 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1sin(3\u03c0x - 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": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((-1(-5x + 3) - 1)/(-2(-5x + 3) + 3))^2 + 4((-1(-5x + 3) - 1)/(-2(-5x + 3) + 3)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-3sin(1\u03c0x + 2) - 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": "Determine the number of values x in [-10, 10] where f(x) = (1(3cos(1\u03c0(-2(-5x)^2 - 1(-5x) - 5) + 1) + 2) - 1)/(1(3cos(1\u03c0(-2(-5x)^2 - 1(-5x) - 5) + 1) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "726", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-3(2x^2 - 4x - 3) - 2)/(1(2x^2 - 4x - 3) + 3)) - 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 zeros does the function f(x) = (2(2sin(3\u03c0(-1(-3|x - 3| + 1) + 4) + 2) - 1) + 2)/(3(2sin(3\u03c0(-1(-3|x - 3| + 1) + 4) + 2) - 1) - 1) have in the interval [-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) = (-2(-1|(-5x^2 + 2x + 3) + 3| + 2) - 2)/(3(-1|(-5x^2 + 2x + 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": "How many zeros does the function f(x) = -4(2|x|)^2 - 1(2|x|) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5((-1(-2|x + 3| + 1) - 1)/(-3(-2|x + 3| + 1) + 4)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1(-3|((-3x + 1)/(2x - 3)) - 1| + 1) - 3)^2 - 3(-1(-3|((-3x + 1)/(2x - 3)) - 1| + 1) - 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": "How many solutions does the equation (1(2(-1x - 3)^2 + 5(-1x - 3) - 4) - 2)/(-3(2(-1x - 3)^2 + 5(-1x - 3) - 4) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(2\u03c0(-1|(2x - 3) - 2|) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2|(3((-3x + 3)/(3x + 2)) + 4) + 1| - 3)^2 - 4(-2|(3((-3x + 3)/(3x + 2)) + 4) + 1| - 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(2(-2(1sin(1\u03c0x)) + 4)^2 - 5(-2(1sin(1\u03c0x)) + 4) + 2) + 2)/(1(2(-2(1sin(1\u03c0x)) + 4)^2 - 5(-2(1sin(1\u03c0x)) + 4) + 2) + 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 1|((-1(1(1x - 1)^2 - 5(1x - 1) - 1) - 3)/(-3(1(1x - 1)^2 - 5(1x - 1) - 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(-3sin(3\u03c0(-3|(1x + 2) + 3| + 3)) - 3) - 1)/(2(-3sin(3\u03c0(-3|(1x + 2) + 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": "178", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((-1(-3(-1|x| + 3)^2 + 1(-1|x| + 3)))/(3(-3(-1|x| + 3)^2 + 1(-1|x| + 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) = -3sin(1\u03c0(1|(-1x - 1) + 3|) + 1) + 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 1((-1(-2|x - 2| + 3) - 1)/(-3(-2|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2|(3cos(3\u03c0x + 2) + 1) - 3| + 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2sin(3\u03c0(-4x^2 - 1x + 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1583", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(5(-3|(-3x + 5) - 2|)^2 - 2(-3|(-3x + 5) - 2|) - 1) + 1)/(2(5(-3|(-3x + 5) - 2|)^2 - 2(-3|(-3x + 5) - 2|) - 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(1|x + 1| + 3) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(2|x - 3|)^2 + 4(2|x - 3|) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(2sin(2\u03c0(-5((-3x - 1)/(3x))) + 3) - 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 solutions does the equation -3((-2(4(2|x + 2| - 2) + 4) - 3)/(-1(4(2|x + 2| - 2) + 4) - 3))^2 + 4((-2(4(2|x + 2| - 2) + 4) - 3)/(-1(4(2|x + 2| - 2) + 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 zeros does the function f(x) = 1|(-3((-1(-2x^2 + 5x - 5) - 2)/(1(-2x^2 + 5x - 5) + 1)) + 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(1\u03c0(-3((1x + 3)/(3x)) + 4) + 1) + 1 = 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": "Determine the number of values x in [-10, 10] where f(x) = 1(-5x + 2)^2 - 5(-5x + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(1|x + 3| - 1) - 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) = -2|(-2x^2 - 5x - 1) + 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) = -3|((1(-2(1x^2 + 2x - 1) - 4) - 1)/(2(-2(1x^2 + 2x - 1) - 4) + 1)) - 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 -1(2cos(3\u03c0x + 3) - 2) - 4 = 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 2|((1(-1(-4x)^2 - 1(-4x) + 4) - 1)/(-2(-1(-4x)^2 - 1(-4x) + 4) + 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": "How many zeros does the function f(x) = 3sin(2\u03c0(-5x - 4) - 2) - 2 have in the interval [-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) = -2|((-1(1(-2x^2 - 4x - 1)) - 2)/(2(1(-2x^2 - 4x - 1)) + 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|((1(-3(-2x^2 + 1x + 5) - 1) + 1)/(1(-3(-2x^2 + 1x + 5) - 1))) + 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 -3cos(2\u03c0((2(-1x) + 1)/(1(-1x))) - 2) + 1 = 0 have in the range [-10, 10]?\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) = 5(-3((-1x - 3)/(1x - 3)) + 4)^2 - 5(-3((-1x - 3)/(1x - 3)) + 4) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(1((2x + 1)/(-1x + 2)) + 2)^2 - 5(1((2x + 1)/(-1x + 2)) + 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4((2(3(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) - 4) - 3)/(-1(3(-1|x - 2| + 3)^2 + 1(-1|x - 2| + 3) - 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": "How many zeros does the function f(x) = -4(1e^(2(-3|(-3x^2 - 2x) + 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) = (-2(2(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 3) - 5) + 1)/(3(2(-1|x + 2| + 3)^2 + 4(-1|x + 2| + 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": "How many zeros does the function f(x) = (3(2|x + 1| - 1) + 1)/(-1(2|x + 1| - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(3|(-1x - 1) + 1|)^2 - 4(3|(-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": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-2cos(1\u03c0((2x + 1)/(1x - 2)) - 2) + 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(2(-3|x - 2| + 2) + 3) + 2)/(-1(2(-3|x - 2| + 2) + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-3|((2(2x + 2) - 1)/(3(2x + 2))) + 2| + 3)^2 + 2(-3|((2(2x + 2) - 1)/(3(2x + 2))) + 2| + 3) - 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) = (-3(-3x^2 - 1x + 2) + 3)/(1(-3x^2 - 1x + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(3sin(3\u03c0(-1x + 3) - 3) - 3) + 2)/(3(3sin(3\u03c0(-1x + 3) - 3) - 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2e^(-1(2(-1x)^2 + 5(-1x) + 4)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(3sin(2\u03c0(2|(-5x - 5) - 2| - 2) + 2) + 2)^2 - 5(3sin(2\u03c0(2|(-5x - 5) - 2| - 2) + 2) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(1|(1((1x - 2)/(-1x - 1)) - 4) + 2| - 2)^2 + 1(1|(1((1x - 2)/(-1x - 1)) - 4) + 2| - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1sin(2\u03c0(2x + 2)) - 1 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": "How many solutions does the equation 1sin(3\u03c0(-5(-3|((1x - 1)/(2x - 1)) - 1| + 1)^2 - 2(-3|((1x - 1)/(2x - 1)) - 1| + 1) + 5)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "78", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(3cos(1\u03c0(5x^2 - 4) - 2) + 3) + 3)/(-2(3cos(1\u03c0(5x^2 - 4) - 2) + 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "948", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0((3(1|(-2x^2 - 3x - 5) - 3|) + 1)/(-3(1|(-2x^2 - 3x - 5) - 3|) + 4)) - 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) = 2|(-4((1x - 3)/(-3x - 3))) + 1| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3|((3x - 3)/(2x - 3)) - 2| - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-5(2e^(1((-3x + 1)/(-2x - 2))) - 1)^2 + 1(2e^(1((-3x + 1)/(-2x - 2))) - 1) + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(2|(2cos(2\u03c0(4x + 2) + 2) + 1) + 3|)^2 + 4(2|(2cos(2\u03c0(4x + 2) + 2) + 1) + 3|) + 4 = 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) = 3(-1sin(2\u03c0x + 3) + 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(5(-2((2x - 2)/(3x - 2))^2 + 5((2x - 2)/(3x - 2)) - 1) - 2) - 2| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-1(-3|(-2x + 1) - 1| + 1)^2 + 2(-3|(-2x + 1) - 1| + 1) + 5) + 1)/(3(-1(-3|(-2x + 1) - 1| + 1)^2 + 2(-3|(-2x + 1) - 1| + 1) + 5) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(3cos(1\u03c0x + 1) + 1) - 1)/(1(3cos(1\u03c0x + 1) + 1) + 2) 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) = 1((-3(-1x + 1))/(1(-1x + 1) - 3))^2 - 1((-3(-1x + 1))/(1(-1x + 1) - 3)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-3|(3(-3e^(1x) + 3)^2 + 5(-3e^(1x) + 3) - 4) + 2| + 1) - 1)/(1(-3|(3(-3e^(1x) + 3)^2 + 5(-3e^(1x) + 3) - 4) + 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(3\u03c0(2x - 2) + 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 1e^(2(5(1x^2 - 5x - 1) + 5)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(2sin(3\u03c0((1(-1|x + 2| - 1))/(-1(-1|x + 2| - 1) - 2)) + 1))^2 + 3(2sin(3\u03c0((1(-1|x + 2| - 1))/(-1(-1|x + 2| - 1) - 2)) + 1)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "223", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1cos(1\u03c0(-2|x - 2| - 3) - 1) + 2)^2 - 4(-1cos(1\u03c0(-2|x - 2| - 3) - 1) + 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": "Determine the number of values x in [-10, 10] where f(x) = 1(-1(3|x - 3| - 3)^2 - 3(3|x - 3| - 3) + 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(3cos(1\u03c0(-1x + 4)) + 2)^2 + 5(3cos(1\u03c0(-1x + 4)) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(1cos(2\u03c0x + 2) + 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": "How many solutions does the equation 1sin(2\u03c0(-5(-1x^2 - 1x + 2) + 5) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "840", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1|((-3x + 3)/(1x - 3))| + 1) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-3sin(3\u03c0(3x^2 + 3x + 4) + 1) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "965", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(5(2|(-5x) - 2| - 2)^2 + 4(2|(-5x) - 2| - 2) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1552", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1e^(-1(1(-1x^2 + 1x + 1) + 4)) - 1) + 3)/(-3(1e^(-1(1(-1x^2 + 1x + 1) + 4)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(2cos(1\u03c0x) + 1) - 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 solutions does the equation 1(2|(-3x^2 + 5x - 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": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(1((-3(-2|x - 2| - 3) - 3)/(-1(-2|x - 2| - 3) + 2)))^2 + 5(1((-3(-2|x - 2| - 3) - 3)/(-1(-2|x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(2sin(3\u03c0(-5x^2 + 5x - 5)) - 1) + 3)/(-2(2sin(3\u03c0(-5x^2 + 5x - 5)) - 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "739", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(1\u03c0(1x^2 + 3x - 5)) - 2 equals zero.\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) = 2(-3|(-3(1e^(1x) - 3) - 1) + 3| + 2)^2 - 1(-3|(-3(1e^(1x) - 3) - 1) + 3| + 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) = -5((-3(-2|x + 1| - 1) - 3)/(-1(-2|x + 1| - 1) + 2)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-2|(-4((3x - 2)/(2x - 1))^2 - 3((3x - 2)/(2x - 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": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-3x^2 + 4x + 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"}