data_source stringclasses 1
value | prompt listlengths 1 1 | ability stringclasses 1
value | reward_model dict | extra_info dict |
|---|---|---|---|---|
DeepScaleR | [
{
"role": "user",
"content": "Calculate the expression $\\left(100 - \\left(5000 - 500\\right)\\right) \\times \\left(5000 - \\left(500 - 100\\right)\\right)$."
}
] | math | {
"style": "rule",
"ground_truth": "-20240000"
} | {
"index": 5700,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following expression (accurate to 8 decimal places):\n$$\n16\\left(\\frac{1}{5}-\\frac{1}{3} \\times \\frac{1}{5^{3}}+\\frac{1}{5} \\times \\frac{1}{5^{5}}-\\frac{1}{7} \\times \\frac{1}{5^{7}}+\\frac{1}{9} \\times \\frac{1}{5^{9}}-\\frac{1}{11} \\times \\frac{1}{... | math | {
"style": "rule",
"ground_truth": "3.14159265"
} | {
"index": 5701,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following expression:\n$$2(1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2(1+2))))))))))$$"
}
] | math | {
"style": "rule",
"ground_truth": "4094"
} | {
"index": 5702,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following expression:\n\\[\\left( 1 - \\frac{1}{\\cos 30^\\circ} \\right) \\left( 1 + \\frac{1}{\\sin 60^\\circ} \\right) \\left( 1 - \\frac{1}{\\sin 30^\\circ} \\right) \\left( 1 + \\frac{1}{\\cos 60^\\circ} \\right).\\]"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5703,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following expressions:\n1. $(-51) + (-37)$;\n2. $(+2) + (-11)$;\n3. $(-12) + (+12)$;\n4. $8 - 14$;\n5. $15 - (-8)$;\n6. $(-3.4) + 4.3$;\n7. $|-2\\frac{1}{4}| + (-\\frac{1}{2})$;\n8. $-4 \\times 1\\frac{1}{2}$;\n9. $-3 \\times (-6)$."
}
] | math | {
"style": "rule",
"ground_truth": "18"
} | {
"index": 5704,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following infinite product: $3^{\\frac{1}{3}} \\cdot 9^{\\frac{1}{9}} \\cdot 27^{\\frac{1}{27}} \\cdot 81^{\\frac{1}{81}} \\dotsm.$"
}
] | math | {
"style": "rule",
"ground_truth": "3^{\\frac{3}{4}}"
} | {
"index": 5705,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following powers to 4 decimal places:\na) \\(1.02^{30}\\)\nb) \\(0.996^{13}\\)"
}
] | math | {
"style": "rule",
"ground_truth": "0.9492"
} | {
"index": 5706,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following product:\n$$\\frac{1}{3}\\times9\\times\\frac{1}{27}\\times81\\times\\frac{1}{243}\\times729\\times\\frac{1}{2187}\\times6561\\times\\frac{1}{19683}\\times59049.$$"
}
] | math | {
"style": "rule",
"ground_truth": "243"
} | {
"index": 5707,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following product: $12 \\times 0.5 \\times 3 \\times 0.2 =$\nA) $\\frac{20}{5}$\nB) $\\frac{22}{5}$\nC) $\\frac{16}{5}$\nD) $\\frac{18}{5}$\nE) $\\frac{14}{5}$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{18}{5}"
} | {
"index": 5708,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the following value expressed as a common fraction: $$\\frac{1}{4^{1}}+\\frac{1}{4^{2}}+\\frac{1}{4^{3}}+\\frac{1}{4^{4}}+\\frac{1}{4^{5}}+\\frac{1}{4^{6}}+\\frac{1}{4^{7}}.$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{16383}{49152}"
} | {
"index": 5709,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the force with which water presses on a dam, whose cross-section has the shape of an isosceles trapezoid. The density of water is $\\rho=1000 \\, \\text{kg} / \\text{m}^{3}$, and the acceleration due to gravity $g$ is $10 \\, \\text{m} / \\text{s}^{2}$.\n\nHint: The p... | math | {
"style": "rule",
"ground_truth": "640000"
} | {
"index": 5710,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the greatest common divisor (GCD) of the numbers 4557, 1953, and 5115."
}
] | math | {
"style": "rule",
"ground_truth": "93"
} | {
"index": 5711,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the greatest integer less than or equal to $\\frac{5^{98} + 2^{104}}{5^{95} + 2^{101}}$."
}
] | math | {
"style": "rule",
"ground_truth": "125"
} | {
"index": 5712,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the harmonic mean of the numbers $1999$ and $2001$."
}
] | math | {
"style": "rule",
"ground_truth": "2000"
} | {
"index": 5713,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the infinite sum:\n\\[\n\\sum_{n=1}^\\infty \\frac{n^3 - n}{(n+3)!}\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{6}"
} | {
"index": 5714,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integer nearest to $500\\sum_{n=4}^{10005}\\frac{1}{n^2-9}$."
}
] | math | {
"style": "rule",
"ground_truth": "174"
} | {
"index": 5715,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integral\n\n$$\n\\int_{0}^{0.1} \\cos \\left(100 x^{2}\\right) d x\n$$\n\nwith an accuracy of $\\alpha=0.001$."
}
] | math | {
"style": "rule",
"ground_truth": "0.090"
} | {
"index": 5716,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integral $\\int_{2}^{7}(x-3)^{2} d x$.\n\na) Using the substitution $z=x-3$.\n\nb) Using the substitution $z=(x-3)^{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{65}{3}"
} | {
"index": 5717,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integral \\(\\int_{0}^{2}\\left(x^{2}+x-1\\right) e^{x / 2} \\, d x\\)."
}
] | math | {
"style": "rule",
"ground_truth": "2 (3e - 5)"
} | {
"index": 5718,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integral \\(\\int_{0}^{\\pi / 2} \\frac{\\sin^{3} x}{2 + \\cos x} \\, dx\\)."
}
] | math | {
"style": "rule",
"ground_truth": "3 \\ln \\left(\\frac{2}{3}\\right) + \\frac{3}{2}"
} | {
"index": 5719,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integrals:\n1) $\\int_{0}^{1} x e^{-x} \\, dx$\n2) $\\int_{1}^{2} x \\log_{2} x \\, dx$\n3) $\\int_{1}^{e} \\ln^{2} x \\, dx$"
}
] | math | {
"style": "rule",
"ground_truth": "e - 2"
} | {
"index": 5720,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the integrals:\n1) \\(\\int_{0}^{\\frac{\\pi}{2}} \\sin ^{3} x \\, dx\\);\n2) \\(\\int_{0}^{\\ln 2} \\sqrt{e^{x}-1} \\, dx\\);\n3) \\(\\int_{-a}^{a} x^{2} \\sqrt{a^{2}-x^{2}} \\, dx\\);\n4) \\(\\int_{1}^{2} \\frac{\\sqrt{x^{2}-1}}{x} \\, dx\\)."
}
] | math | {
"style": "rule",
"ground_truth": "\\sqrt{3} - \\frac{\\pi}{3}"
} | {
"index": 5721,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the largest prime factor of $18^4 + 12^5 - 6^6$."
}
] | math | {
"style": "rule",
"ground_truth": "11"
} | {
"index": 5722,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the length of the arc of the astroid given by \\(x=\\cos^{3} t\\), \\(y=\\sin^{3} t\\), where \\(0 \\leq t \\leq 2\\pi\\)."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5723,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of arcs of curves given by equations in polar coordinates.\n\n$$\n\\rho = 3(1 + \\sin \\varphi), -\\frac{\\pi}{6} \\leq \\varphi \\leq 0\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "6(\\sqrt{3} - \\sqrt{2})"
} | {
"index": 5724,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of arcs of curves given by the parametric equations.\n\n$$\n\\begin{aligned}\n& \\left\\{\\begin{array}{l}\nx=2(t-\\sin t) \\\\\ny=2(1-\\cos t)\n\\end{array}\\right. \\\\\n& 0 \\leq t \\leq \\frac{\\pi}{2}\n\\end{aligned}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "8 - 4\\sqrt{2}"
} | {
"index": 5725,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of the arcs of curves defined by the equations in polar coordinates.\n\n$$\n\\rho=5(1-\\cos \\varphi),-\\frac{\\pi}{3} \\leq \\varphi \\leq 0\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "20 \\left(1 - \\frac{\\sqrt{3}}{2}\\right)"
} | {
"index": 5726,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of the arcs of curves given by the equations in the rectangular coordinate system.\n\n$$\ny=\\ln x, \\sqrt{3} \\leq x \\leq \\sqrt{15}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} \\ln \\frac{9}{5} + 2"
} | {
"index": 5727,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of the arcs of the curves given by the equations in polar coordinates.\n\n$$\n\\rho = 2 \\varphi, \\; 0 \\leq \\varphi \\leq \\frac{4}{3}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{20}{9} + \\ln 3"
} | {
"index": 5728,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of the arcs of the curves given by the equations in the rectangular coordinate system.\n\n\\[ y = \\ln \\frac{5}{2 x}, \\quad \\sqrt{3} \\leq x \\leq \\sqrt{8} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "1 + \\frac{1}{2} \\ln \\frac{3}{2}"
} | {
"index": 5729,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the lengths of the arcs of the curves given by the parametric equations.\n\n$$\n\\begin{aligned}\n& \\left\\{\\begin{array}{l}\nx=\\left(t^{2}-2\\right) \\sin t+2 t \\cos t \\\\\ny=\\left(2-t^{2}\\right) \\cos t+2 t \\sin t\n\\end{array}\\right. \\\\\n& 0 \\leq t \\le... | math | {
"style": "rule",
"ground_truth": "\\frac{8\\pi^3}{3}"
} | {
"index": 5730,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit\n\n$$\n\\lim _{x \\rightarrow 0}\\left(\\frac{1+x^{2} 2^{x}}{1+x^{2} 5^{x}}\\right)^{1 / \\sin ^{3} x}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{5}"
} | {
"index": 5731,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 0} \\ln \\left(\\left(e^{x^{2}}-\\cos x\\right) \\cos \\left(\\frac{1}{x}\\right)+\\operatorname{tg}\\left(x+\\frac{\\pi}{3}\\right)\\right)\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{2} \\ln (3)"
} | {
"index": 5732,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 0}(1-\\ln (1+\\sqrt[3]{x}))^{\\frac{x}{\\sin ^{4} \\sqrt[3]{x}}}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "e^{-1}"
} | {
"index": 5733,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 0}\\left(3-\\frac{2}{\\cos x}\\right)^{\\operatorname{cosec}^{2} x}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "e^{-1}"
} | {
"index": 5734,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim _{x \\rightarrow 1}\\left(\\frac{e^{\\sin \\pi x}-1}{x-1}\\right)^{x^{2}+1}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\pi^2"
} | {
"index": 5735,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\n\\lim_{x \\rightarrow 1} (2-x)^{\\sin \\left(\\frac{\\pi x}{2}\\right) / \\ln (2-x)}\n$$"
}
] | math | {
"style": "rule",
"ground_truth": "e"
} | {
"index": 5736,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow 0} \\frac{3^{5 x}-2^{x}}{x-\\sin 9 x}$$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{8} \\ln \\frac{2}{243}"
} | {
"index": 5737,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow 0} \\frac{e^{4 x}-1}{\\sin \\left(\\pi\\left(\\frac{x}{2}+1\\right)\\right)}$$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{8}{\\pi}"
} | {
"index": 5738,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow 0}\\left(\\frac{\\arcsin ^{2} x}{\\arcsin ^{2} 4 x}\\right)^{2 x+1}$$"
}
] | math | {
"style": "rule",
"ground_truth": "1/16"
} | {
"index": 5739,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\\lim _{x \\rightarrow \\pi}\\left(\\operatorname{ctg}\\left(\\frac{x}{4}\\right)\\right)^{1 / \\cos \\left(\\frac{x}{2}\\right)}$$"
}
] | math | {
"style": "rule",
"ground_truth": "e"
} | {
"index": 5740,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$$\\lim_{x \\rightarrow \\frac{1}{3}} \\frac{\\sqrt[3]{\\frac{x}{9}}-\\frac{1}{3}}{\\sqrt{\\frac{1}{3}+x}-\\sqrt{2x}}$$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{2 \\sqrt{2}}{3 \\sqrt{3}}"
} | {
"index": 5741,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$\\lim _{x \\rightarrow \\frac{1}{4}} \\frac{\\sqrt[3]{\\frac{x}{16}}-\\frac{1}{4}}{\\sqrt{\\frac{1}{4}+x}-\\sqrt{2x}}$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{2\\sqrt{2}}{6}"
} | {
"index": 5742,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n$\\lim _{x \\rightarrow \\pi} \\frac{\\sin \\left(\\frac{x^{2}}{\\pi}\\right)}{2^{\\sqrt{\\sin x+1}}-2}$"
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{\\ln 2}"
} | {
"index": 5743,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n\\[\n\\lim_{x \\rightarrow 0} \\frac{\\arcsin(2x)}{2^{-3x} - 1} \\cdot \\ln 2\n\\]"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{2}{3}"
} | {
"index": 5744,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\n\\[ \\lim _{x \\rightarrow \\frac{1}{2}} \\frac{\\sqrt[3]{\\frac{x}{4}}-\\frac{1}{2}}{\\sqrt{\\frac{1}{2}+x}-\\sqrt{2x}} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{2}{3}"
} | {
"index": 5745,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the function:\n\\[ \\lim _{x \\rightarrow \\frac{\\pi}{3}} \\frac{1-2 \\cos x}{\\sin (\\pi-3 x)} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{\\sqrt{3}}{3}"
} | {
"index": 5746,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the numerical sequence:\n\n$$\\lim _{n \\rightarrow \\infty} \\frac{\\sqrt[4]{2+n^{5}}-\\sqrt{2 n^{3}+3}}{(n+\\sin n) \\sqrt{7 n}}$$"
}
] | math | {
"style": "rule",
"ground_truth": "-\\sqrt{\\frac{2}{7}}"
} | {
"index": 5747,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the limit of the numerical sequence:\n\n$$\\lim _{n \\rightarrow \\infty} \\frac{\\sqrt{n+6}-\\sqrt{n^{2}-5}}{\\sqrt[3]{n^{3}+3}+\\sqrt[4]{n^{3}+1}}$$"
}
] | math | {
"style": "rule",
"ground_truth": "-1"
} | {
"index": 5748,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the line integral\n\n$$\n\\int_{L} \\frac{y}{3} d x - 3 x d y + x d z\n$$\n\nalong the curve \\( L \\), which is given parametrically by\n\n$$\n\\begin{cases}\nx = 2 \\cos t \\\\\ny = 2 \\sin t \\\\\nz = 1 - 2 \\cos t - 2 \\sin t\n\\end{cases}\n\\quad \\text{for} \\qu... | math | {
"style": "rule",
"ground_truth": "2 - \\frac{13\\pi}{3}"
} | {
"index": 5749,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the minimum number of digits to the right of the decimal point needed to express the fraction $\\frac{987654321}{2^{30} \\cdot 5^6 \\cdot 3}$."
}
] | math | {
"style": "rule",
"ground_truth": "30"
} | {
"index": 5750,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the minimum of $\\sqrt{(x-1)^{2}+y^{2}}+\\sqrt{(x+1)^{2}+y^{2}}+|2-y|$ for $x, y \\in \\mathbb{R}$."
}
] | math | {
"style": "rule",
"ground_truth": "2 + \\sqrt{3}"
} | {
"index": 5751,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the monotonic intervals of $F(x)=\\int_{0}^{x}{(t^{2}+2t-8)dt}$ for $x > 0$.\n\n(1) Determine the monotonic intervals of $F(x)$.\n\n(2) Find the maximum and minimum values of the function $F(x)$ on the interval $[1,2]$."
}
] | math | {
"style": "rule",
"ground_truth": "-\\frac{28}{3}"
} | {
"index": 5752,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the nearest integer to $(3+\\sqrt{5})^6$."
}
] | math | {
"style": "rule",
"ground_truth": "20608"
} | {
"index": 5753,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of different rectangles with sides parallel to the grid that can be formed by connecting four of the dots in a $5\\times 5$ square array of dots. (Two rectangles are different if they do not share all four vertices.)"
}
] | math | {
"style": "rule",
"ground_truth": "100"
} | {
"index": 5754,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of distinct three-digit numbers formed using the digits 0, 1, 2, 3, 4, and 5 without repetition that are divisible by 9."
}
] | math | {
"style": "rule",
"ground_truth": "16"
} | {
"index": 5755,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of five-digit numbers formed from the digits 1, 2, 3, 4, 5 without repeating any digits, and where the digits 1 and 2 are not adjacent to the digit 5."
}
] | math | {
"style": "rule",
"ground_truth": "36"
} | {
"index": 5756,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of four-digit numbers without repeating digits that can be formed by taking any two odd numbers and two even numbers from the six digits 0, 1, 2, 3, 4, 5."
}
] | math | {
"style": "rule",
"ground_truth": "180"
} | {
"index": 5757,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of minutes in a week."
}
] | math | {
"style": "rule",
"ground_truth": "10000"
} | {
"index": 5758,
"solution": "There are 60 minutes in an hour and 24 hours in a day. Thus, there are $60 \\cdot 24=1440$ minutes in a day. Since there are 7 days in a week, the number of minutes in a week is $7 \\cdot 1440=10080$. Of the given choices, this is closest to 10000."
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of multiples of 4 that are between 100 and 500."
}
] | math | {
"style": "rule",
"ground_truth": "99"
} | {
"index": 5759,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of multiplication and addition operations needed to compute the value of the polynomial $f(x) = 3x^6 + 4x^5 + 5x^4 + 6x^3 + 7x^2 + 8x + 1$ at $x = 0.7$ using the Horner's method."
}
] | math | {
"style": "rule",
"ground_truth": "12"
} | {
"index": 5760,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of seven-digit palindromes where the second digit cannot be odd."
}
] | math | {
"style": "rule",
"ground_truth": "4500"
} | {
"index": 5761,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of terms in the simplified expression of \\[(x+y+z)^{2020} + (x-y-z)^{2020},\\] by expanding it and combining like terms."
}
] | math | {
"style": "rule",
"ground_truth": "1,022,121"
} | {
"index": 5762,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the number of zeros at the end of 2015!."
}
] | math | {
"style": "rule",
"ground_truth": "502"
} | {
"index": 5763,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the numerical value by listing.<br/>Select $5$ people from $8$ people including $A$, $B$, and $C$ to line up.<br/>$(1)$ If $A$ must be included, how many ways are there to line up?<br/>$(2)$ If $A$, $B$, and $C$ are not all included, how many ways are there to line up... | math | {
"style": "rule",
"ground_truth": "4440"
} | {
"index": 5764,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the percentage of five-digit numbers that have at least one repeated digit (the repeated digits do not need to be adjacent). Express your answer as a decimal to the nearest tenth."
}
] | math | {
"style": "rule",
"ground_truth": "69.8"
} | {
"index": 5765,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the perimeter of a triangle whose vertices are located at points $A(2,3)$, $B(2,10)$, and $C(8,6)$ on a Cartesian coordinate plane."
}
] | math | {
"style": "rule",
"ground_truth": "7 + 2\\sqrt{13} + 3\\sqrt{5}"
} | {
"index": 5766,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the positive difference between $\\frac{7^3 + 7^3}{7}$ and $\\frac{(7^3)^2}{7}$."
}
] | math | {
"style": "rule",
"ground_truth": "16709"
} | {
"index": 5767,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability of a contestant winning the quiz given that they answer at least 3 out of 4 questions correctly, assuming random guesses for each question with 3 possible answer options."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{9}"
} | {
"index": 5768,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability of selecting the letter \"$s$\" in the word \"statistics\"."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{3}{10}"
} | {
"index": 5769,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability of the Alphas winning given the probability of the Reals hitting 0, 1, 2, 3, or 4 singles."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{224}{243}"
} | {
"index": 5770,
"solution": "The probability of the Reals hitting 0 singles is $\\left(\\frac{2}{3}\\right)^{3}$. The probability of the Reals hitting exactly 1 single is $\\binom{3}{2} \\cdot\\left(\\frac{2}{3}\\right)^{3} \\cdot \\frac{1}{3}$, since there are 3 spots to put the two outs (the last spot must be an... |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that all the rational terms are not adjacent to each other when rearranging the terms of the expansion $( \\sqrt {x}+ \\dfrac {1}{2 \\sqrt[4]{x}})^{8}$ in a list."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{5}{12}"
} | {
"index": 5771,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that athlete A cannot run the first leg and athlete B cannot run the last leg in a 4x100 meter relay race selection from 6 short-distance runners, including athletes A and B, to form a team of 4 runners."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{7}{10}"
} | {
"index": 5772,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that four randomly chosen vertices of a cube form a tetrahedron (triangular pyramid)."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{29}{35}"
} | {
"index": 5773,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that in a deck of 52 cards, the second card has a different suit than the first, and the third card has a different suit than the first and second."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{169}{425}"
} | {
"index": 5774,
"solution": "The probability that the second card has a different suit than the first is $\\frac{3 \\cdot 13}{52-1}$. The probability that the third card has a different suit than the first and second card is $\\frac{2 \\cdot 13}{52-2}$. Since the two events need to both occur, we use the multiplic... |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that in a family where there is already one child who is a boy, the next child will also be a boy."
}
] | math | {
"style": "rule",
"ground_truth": "1/3"
} | {
"index": 5775,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that the line $y=kx+k$ intersects with the circle ${{\\left( x-1 \\right)}^{2}}+{{y}^{2}}=1$."
}
] | math | {
"style": "rule",
"ground_truth": "\\dfrac{1}{3}"
} | {
"index": 5776,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the probability that the numbers 1, 1, 2, 2, 3, 3 can be arranged into two rows and three columns such that no two identical numbers appear in the same row or column."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{15}"
} | {
"index": 5777,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product $(\\frac{4}{8})(\\frac{8}{12})(\\frac{12}{16})\\cdots(\\frac{2016}{2020})$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{505}"
} | {
"index": 5778,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product $\\left(\\frac{3}{6}\\right)\\left(\\frac{6}{9}\\right)\\left(\\frac{9}{12}\\right)\\cdots\\left(\\frac{2001}{2004}\\right)$. Express your answer as a common fraction."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{1}{668}"
} | {
"index": 5779,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product of $1101_2 \\cdot 111_2$. Express your answer in base 2."
}
] | math | {
"style": "rule",
"ground_truth": "1100111_2"
} | {
"index": 5780,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product of $\\frac{5}{3} \\times \\frac{6}{5} \\times \\frac{7}{6} \\times \\cdots \\times \\frac{2010}{2009}$."
}
] | math | {
"style": "rule",
"ground_truth": "670"
} | {
"index": 5781,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product of all prime numbers between 1 and 20."
}
] | math | {
"style": "rule",
"ground_truth": "9699690"
} | {
"index": 5782,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product of the base nine numbers $35_9$ and $47_9$, express it in base nine, and find the base nine sum of the digits of this product. Additionally, subtract $2_9$ from the sum of the digits."
}
] | math | {
"style": "rule",
"ground_truth": "22_9"
} | {
"index": 5783,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product: $100 \\times 29.98 \\times 2.998 \\times 1000 = $"
}
] | math | {
"style": "rule",
"ground_truth": "2998^2"
} | {
"index": 5784,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the product: $500 \\times 2019 \\times 0.02019 \\times 5.$"
}
] | math | {
"style": "rule",
"ground_truth": "0.25 \\times 2019^2"
} | {
"index": 5785,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the radius of the circle where all the complex roots of the equation $(z - 1)^6 = 64z^6$ lie when plotted in the complex plane."
}
] | math | {
"style": "rule",
"ground_truth": "\\frac{2}{3}"
} | {
"index": 5786,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the remainder when $1 + 11 + 11^2 + \\cdots + 11^{1024}$ is divided by $500$."
}
] | math | {
"style": "rule",
"ground_truth": "25"
} | {
"index": 5787,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the remainder when the sum $100001 + 100002 + \\cdots + 100010$ is divided by 11."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5788,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the result of the expression \\( 2015 \\frac{1999}{2015} \\times \\frac{1}{4} - \\frac{2011}{2015} \\)."
}
] | math | {
"style": "rule",
"ground_truth": "503"
} | {
"index": 5789,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the result of the expression \\((19 \\times 19 - 12 \\times 12) \\div \\left(\\frac{19}{12} - \\frac{12}{19}\\right)\\)."
}
] | math | {
"style": "rule",
"ground_truth": "228"
} | {
"index": 5790,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the result of the expression:\n\n\\[ 2013 \\times \\frac{5.7 \\times 4.2 + \\frac{21}{5} \\times 4.3}{\\frac{14}{73} \\times 15 + \\frac{5}{73} \\times 177 + 656} \\]"
}
] | math | {
"style": "rule",
"ground_truth": "126"
} | {
"index": 5791,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the roundness of 1,728,000."
}
] | math | {
"style": "rule",
"ground_truth": "19"
} | {
"index": 5792,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the smallest root \\(x_0\\) of the equation\n\n$$\nx^{2}-\\sqrt{\\lg x +100}=0\n$$\n\n(with a relative error of no more than \\(10^{-390} \\%\\))."
}
] | math | {
"style": "rule",
"ground_truth": "10^{-100}"
} | {
"index": 5793,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the square of 1007 without using a calculator."
}
] | math | {
"style": "rule",
"ground_truth": "1014049"
} | {
"index": 5794,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum $1 + 3 + 5 + \\cdots + 15 + 17$."
}
] | math | {
"style": "rule",
"ground_truth": "81"
} | {
"index": 5795,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum $2^{-2} + 2^{-3} + 2^{-4} + 2^{-5} + 2^{-6} + 2^{-7} \\pmod{17}$.\n\nExpress your answer as an integer from $0$ to $16$, inclusive."
}
] | math | {
"style": "rule",
"ground_truth": "10"
} | {
"index": 5796,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum $C_{3}^{2}+C_{4}^{2}+C_{5}^{2}+\\ldots+C_{19}^{2}$."
}
] | math | {
"style": "rule",
"ground_truth": "1139"
} | {
"index": 5797,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum $E(1)+E(2)+E(3)+\\cdots+E(200)$ where $E(n)$ denotes the sum of the even digits of $n$, and $5$ is added to the sum if $n$ is a multiple of $10$."
}
] | math | {
"style": "rule",
"ground_truth": "902"
} | {
"index": 5798,
"solution": ""
} |
DeepScaleR | [
{
"role": "user",
"content": "Calculate the sum $\\frac{3}{50} + \\frac{5}{500} + \\frac{7}{5000}$.\nA) $0.0714$\nB) $0.00714$\nC) $0.714$\nD) $0.0357$\nE) $0.00143$"
}
] | math | {
"style": "rule",
"ground_truth": "0.0714"
} | {
"index": 5799,
"solution": ""
} |
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