prompt list | ground_truth string |
|---|---|
[
{
"content": "Determine whether functions of the form \\( f(x) = \\exp(-x)p(x) \\), where \\( p(x) \\) is a polynomial, can have multiple local maxima.",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether the following claim is true or false: Let $X$ be a normed space, and let $\\{x_1,x_2, \\cdots \\}\\subseteq X$ be a linearly independent subset with $\\alpha_1,\\alpha_2,\\cdots \\in\\mathbb{R}$. Then there exists a functional $f\\in X^*$ such that $f(x_i)=\\alpha_i$ for all $i\\... | False |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $ 86,166.31 |
[
{
"content": "Determine whether it is true that for every natural number $n$ greater than 2, there exists at least one $n \\times n$ magic square.",
"role": "user"
}
] | True |
[
{
"content": "Determine the largest positive real number \\( k \\) such that the inequality \\[ a^3+b^3+c^3-3\\ge k(3-ab-bc-ca) \\] holds for all positive real numbers \\( a, b, c \\) satisfying \\( a+b+c=3. \\)",
"role": "user"
}
] | 5 |
[
{
"content": "In the triangular prism \\( P-ABC \\), where \\( PA \\perp \\) the base \\( ABC \\), \\( \\angle ACB = 90^\\circ \\), \\( AE \\perp PB \\) at \\( E \\), and \\( AF \\perp PC \\) at \\( F \\), given that \\( PA = AB = 2 \\) and \\( \\angle BPC = \\theta \\), find the value of \\(\\tan \\theta\\) wh... | D |
[
{
"content": "How many different positive, six-digit integers can be formed using the digits 2, 2, 5, 5, 9 and 9?",
"role": "user"
}
] | 90 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 209.5ms^-1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 21.5 N |
[
{
"content": "Determine the values of $n$ for which the matrix \\( M = \\begin{bmatrix} n & 1 & 1 \\\\ 1 & n & 1 \\\\ 1 & 1 & -n \\end{bmatrix} \\) is negative definite.",
"role": "user"
}
] | \emptyset |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 60.5 A |
[
{
"content": "Consider a sequence of non-negative random variables $X_n$ that decreases to a non-negative random variable $X$ as $n \\rightarrow \\infty$. Given that $E[X_n] = \\infty$ for all $n$, determine if it is true that $E[X] = \\infty$ under the condition $|X_n - X| \\leq c_n$, where $c_n$ is a sequence... | \infty |
[
{
"content": "Let $X$ be a normed space. Consider elements $x, y \\in X$ such that $x+y \\neq 0$. If \\( \\lim_{n \\to \\infty}\\|(x+y)^n\\|^{\\frac{1}{n}} = 0 \\), does it imply that \\( \\lim_{n \\to \\infty} \\|x^n\\| ^{\\frac{1}{n}} = 0 \\)? Answer yes or no and justify your answer.",
"role": "user"
}... | No |
[
{
"content": "Evaluate the limit: \\[ \\lim_{z\\to 0}\\frac{2z\\sin{z^2}-2z^3\\cos{z^2}}{\\sin^2{z^2}} \\] using the Taylor series expansions for sine and cosine.",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -$10,220.10 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 55400 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.125s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.88e9 J |
[
{
"content": "Calculate the norm of the linear functional $P$ on the space $C[-1,1]$, defined by $P(f) = f(1) + f(-1) - 2f(0)$. What is the norm of $P$?",
"role": "user"
}
] | 4 |
[
{
"content": "What common fraction is exactly half-way between $\\frac{2}{3}$ and $\\frac{4}{5}$?",
"role": "user"
}
] | \frac{11}{15} |
[
{
"content": "Evaluate the definite integral \\( \\int_0^1 f(x) \\, dx \\), where \\( f(x) = \\begin{cases} 2x\\sin\\left(\\frac{1}{x}\\right) - \\cos\\left(\\frac{1}{x}\\right) & : x \\in (0,1] \\\\ 0 & : x = 0 \\end{cases} \\). Determine if the integral is defined, and if so, find its value.",
"role": "us... | \sin 1 |
[
{
"content": "Bag A has 3 white marbles and 4 black marbles. Bag B has 6 yellow marbles and 4 blue marbles. Bag C has 2 yellow marbles and 5 blue marbles. A marble is drawn at random from Bag A. If it is white, a marble is drawn at random from Bag B, otherwise, if it is black, a marble is drawn at random fr... | \frac{103}{245} |
[
{
"content": "In a simple graph $G$ with $mn$ vertices, if each vertex has a degree greater than $m(n-1)$, does $G$ necessarily contain a $K_{n+1}$ subgraph? Answer 'yes' or 'no' and justify your answer.",
"role": "user"
}
] | yes |
[
{
"content": "Let \\( f: \\mathbb{R} \\to \\mathbb{R} \\) be a smooth function that is infinitely differentiable everywhere, with \\( f'(0) = 1 \\) and \\( |f^{(n)}(x)| \\leq 1 \\) for all \\( x \\in \\mathbb{R} \\) and all non-negative integers \\( n \\). Determine whether it is true that \\( f(x) = \\sin(x) \... | \sin(x) |
[
{
"content": "Each page number of a 488-page book is printed one time in the book. The first page is page 1 and the last page is page 488. When printing all of the page numbers, how many more 4's are printed than 8's?",
"role": "user"
}
] | 90 |
[
{
"content": "How many polynomials of degree 3 are contained in the ideal \\( I = (x^5 + x^2 + x + 1, x^7 + x^5 + x^3 + x) \\) in \\( \\mathbb{F}_2[x] \\)?",
"role": "user"
}
] | 2 |
[
{
"content": "Suppose $X$ is a topological space where any two distinct points can be connected by a path that is locally homeomorphic but not necessarily a homeomorphic embedding. Does it follow that $X$ cannot be a Hausdorff space? Answer yes or no and justify your answer.",
"role": "user"
}
] | No |
[
{
"content": "Evaluate the integral \\( \\int \\frac{x^{1/2}}{x^3+1} \\, dx \\) using contour integration.",
"role": "user"
}
] | \dfrac{\pi}{3} |
[
{
"content": "Given a spherical planet X, the angle $A$ from the center of the planet to the outer edge is 3 degrees, and the distance $d$ from your spaceship to the nearest surface of the planet is 100,000 miles. The radius $r$ of the planet is calculated as 5,522.6 miles. After a mishap, your spaceship travel... | 10544 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 142.35 g |
[
{
"content": "A stock trader has 100 shares of a company and uses a random strategy for buying or selling shares based on the outcome of a die roll at each trading session. The strategy is as follows:\n\n- Outcome = 1: Do nothing\n- Outcome = 2 or 4: Buy one share\n- Outcome = 3 or 5: Sell one share\n- Outcome ... | 0.169 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 20 units of capital and 30 units of labor are used to produce 50 units of output. The long-run average cost is $1.4. |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 445.8 mi, 45.5 degrees north of east |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.6 g |
[
{
"content": "Determine whether the following statement is true or false: If a polynomial \\( Q(x) \\) with integer coefficients has the property that \\( Q(n) \\) is a perfect cube for every integer \\( n \\), then the degree of \\( Q(x) \\) must be a multiple of 3.",
"role": "user"
}
] | True |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 64.841 kJ |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $3.29 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.1 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2MnO_4^- + H^+ + 5HNO_2 o 2Mn^{2+} + 5NO_3^- + 3H_2O |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 23% |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.46e-18 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1.07e-17 J |
[
{
"content": "Suppose that for every $\\alpha \\in \\mathbb{R}$, there is a subset $A_\\alpha \\subseteq \\mathbb{R}$ with $|A_\\alpha| = \\mathfrak{c}$. Does there always exist a set $D \\subseteq \\mathbb{R}$ such that $D \\cap A_\\alpha \\neq \\varnothing$ and $A_\\alpha \\nsubseteq D$ for each $\\alpha \\in... | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 555.9 L |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Cash Flow Statement
For the Year Ended December 31, 2013
Cash flows from operating Activities:
Net Income 441,960
Adjustments to net income
Depreciation 63,720
Amortization 12,000
Changes in the current assets and liabilities
Increase in accounts receivables (62,640)
Decrease in inventory 115,440
Increase in prepaid ex... |
[
{
"content": "In an isosceles trapezoid \\(ABCD\\), the diagonals intersect at point \\(M\\). The lateral side \\(AB\\) is perpendicular to the bases \\(AD\\) and \\(BC\\), and a circle can be inscribed in the trapezoid. If the radius of the inscribed circle is \\(r\\), find the area of triangle \\(DCM\\).",
... | r^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 8.345 m/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -11.66 cm/s^2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 542,146 |
[
{
"content": "Consider the sets $X, Y,$ and $Z$ in $\\Bbb R^2$ with the usual topology:\n$$X=\\{(x,y)\\mid x^2+y^2<1\\}\\cup \\{(x,y)\\mid (x-2)^2+y^2<1\\}$$\n$$Y=\\{(x,y)\\mid x^2+y^2<1\\}\\cup \\{(x,y)\\mid (x-3)^2+y^2<1\\}$$\n$$Z=\\{(x,y)\\mid x^2+y^2<1, x\\neq 0\\}$$\nDetermine which of the following option... | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 30 degrees |
[
{
"content": "Evaluate the contour integral \\( \\oint_C \\frac{3}{z + 1 + i}dz \\) where \\( C \\) is the circle \\( |z| = 2 \\).",
"role": "user"
}
] | 6\pi i |
[
{
"content": "For any real numbers $x$ and $y$ satisfying $x^2y + 6y = xy^3 +5x^2 +2x$, it is known that\n\n$$(x^2 + 2xy + 3y^2) \\, f(x,y) = (4x^2 + 5xy + 6y^2) \\, g(x,y)$$\n\nIf $f(1,1) = 10$, find the value of $g(1,1)$. \\( \\boxed{?} \\)",
"role": "user"
}
] | 4 |
[
{
"content": "Find the least non-negative residue of \\(3^{252} \\mod 610\\).",
"role": "user"
}
] | 131 |
[
{
"content": "Determine all real-to-real functions \\( f \\) that satisfy the functional equation:\n\n\\[ f\\left(\\frac{x+y}{x-y}\\right) = \\frac{f(x) + f(y)}{f(x) - f(y)} \\]",
"role": "user"
}
] | f(x) = x |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | Upper and lower sides |F|=0.768N
Both vertical sides |F|=0 |
[
{
"content": "Determine the Jacobson radical of the module $m = {}_B B$, where $B = k[r,s]/(r^2,s^2,rs)$ is a polynomial ring and $k$ is a field.",
"role": "user"
}
] | (r, s) |
[
{
"content": "Let \\(a, b, c\\) be real numbers with \\(a \\neq 0\\). If \\(\\alpha\\) is a root of \\(a^2x^2 + bx + c = 0\\), \\(\\beta\\) is a root of \\(a^2x^2 - bx - c = 0\\), and \\(0 < \\alpha < \\beta\\), determine which of the following statements is correct for the root \\(\\gamma\\) of the equation \\... | D |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 16.85 m |
[
{
"content": "Determine whether the equilibrium states of the following system of differential equations are only possible if $S=0$:\n\n$$ \\begin{aligned} I' &= -bkIS \\\\ S' &= bkIS - akS(S+R) \\\\ R' &= akS(S+R) \\end{aligned} $$\n\nwhere $I'=S'=R'=0$. Provide a justification for your answer.",
"role": "... | Yes |
[
{
"content": "In quadrilateral \\(ABCD\\), where \\(AD \\parallel BC\\), the bisector of angle \\(A\\) intersects side \\(CD\\) at point \\(X\\) and extends side \\(BC\\) beyond point \\(C\\) to point \\(Y\\). Given that \\(\\angle AXC = 90^\\circ\\), \\(AD = 16\\), and \\(CY = 13\\), find the length of segment... | \dfrac{29}{2} |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 13.6 eV |
[
{
"content": "Determine whether there exists a Borel set \\( A \\subset \\mathbb{R}^2 \\) such that its projection onto the first coordinate is not a Borel set in \\( \\mathbb{R} \\).",
"role": "user"
}
] | Yes |
[
{
"content": "Evaluate the integral \\( R(0) = \\frac{1}{2\\pi} \\int_{-\\infty}^{\\infty} \\frac{dk}{ik+1} \\) to find \\( R(0) \\), given that the expected result is \\( R(0) = \\frac{1}{2} \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Consider the set of all square numbers of natural numbers defined in two ways in ZF set theory. Using the axiom of specification, define the set \\( A = \\{n \\in \\mathbb{N} \\mid (\\exists m)(m \\in \\mathbb{N}) \\wedge n = m^2\\} \\). Using the replacement schema with the function \\( F(x) = x^... | A = B |
[
{
"content": "Let $(R, \\mathfrak{m}, k)$ be an Artinian local Gorenstein ring. Consider the category $\\mathcal{F}(R)$ of finitely generated free $R$-modules and the category $\\text{mod}(R)$ of finitely generated $R$-modules. Define the covariant functors $F, G: \\mathcal{F}(R) \\to \\text{mod}(R)$ by $F(-) =... | Yes |
[
{
"content": "Determine the bias of the estimator \\(\\bar{\\theta} = 2\\bar{X} - 1\\), where \\(\\bar{X}\\) is the sample mean of \\(n\\) independent random variables drawn from a uniform distribution \\(U[0,1+\\theta]\\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 2.68 rad/s |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.0e+22 |
[
{
"content": "Let $A$ and $B$ be subsets of $\\mathbb{R}$. Determine whether it is true that $m(A+B) = m(A) + m(B)$, given that the sum $A+B$ is measurable.",
"role": "user"
}
] | False |
[
{
"content": "Given positive rational numbers \\(a, b, c\\) such that \\(a + b + c = abc\\), find the value of the expression:\n\\[\n\\frac{a}{b} + \\frac{a}{c} + \\frac{b}{a} + \\frac{b}{c} + \\frac{c}{a} + \\frac{c}{b} - ab - bc - ca.\n\\]",
"role": "user"
}
] | -3 |
[
{
"content": "Given the sequence defined by $b_{1} = 1$, $b_{2} = 2$, and $b_{n+2} = \\frac{(n+2)b_{n+1}-b_{n}}{(n+1)}$, with the condition $b_{n+1}-b_n = \\frac{1}{n!}$, find the value of $\\lim\\limits_{n \\to +\\infty} b_n$. \\(\\text{Express your answer as a single number.}\\)",
"role": "user"
}
] | e |
[
{
"content": "Given that \\( f(x) \\) is differentiable at \\( x=0 \\) with \\( f(0)=0 \\), \\( f'(0)=1 \\), \\( f''(0)=2 \\), and \\( f^{(n)}(0)\\le \\frac{n!}{2^{n-3}} \\) for \\( n\\ge 3 \\), find the smallest value of \\( m \\) such that \\( f(0.5)\\le m \\).",
"role": "user"
}
] | \dfrac{11}{12} |
[
{
"content": "Calculate the limit: \\[ \\lim_{n \\to \\infty} \\int_{0}^{1} \\frac{ne^{-x}}{1+nx} \\, dx \\]",
"role": "user"
}
] | \infty |
[
{
"content": "Solve the differential equation \\( u''(x) + \\frac{u(x)}{4x^2} = 0 \\) with the boundary conditions \\( u(1) = 0 \\) and \\( u(2) = 0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1292.428 kPa |
[
{
"content": "Find the limit of the sequence \\(y_n=\\frac{a_1}{a_2}\\cdot\\frac{a_3}{a_4}\\cdot...\\cdot\\frac{a_{2n-1}}{a_{2n}}\\) where \\((a_n)_{n\\geq1}\\) is an arithmetic progression such that \\(0<a_1<a_2\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Determine whether it is possible for a satisfiable sentence to have no models of size 4 or greater.",
"role": "user"
}
] | Yes |
[
{
"content": "Find the minimum value of the expression \\(\\frac{(1+x)(x+y)(y+z)(z+4)}{xyz}\\) where \\(x, y, z\\) are positive real numbers.",
"role": "user"
}
] | 17 + 12\sqrt{2} |
[
{
"content": "Let $a, b, c$ be the lengths of the sides of a triangle such that $a + b + c = 3$. Determine the minimum value of the expression $$a^8 + b^8 + c^8 + 2(a-1)(b-1)(c-1).$$",
"role": "user"
}
] | 3 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | V = Bvd |
[
{
"content": "Let $\\omega$ be a complex number such that $|\\omega| = 1,$ and the equation\n\\[z^2 + z + \\omega = 0\\]has a pure imaginary root $z.$ Find $\\omega + \\overline{\\omega}.$",
"role": "user"
}
] | \sqrt{5} - 1 |
[
{
"content": "Determine whether the compactness of a topological space under a finer topology implies its compactness under a coarser topology.",
"role": "user"
}
] | Yes |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | $9 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 32.42 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | -10206.25 |
[
{
"content": "Evaluate the triple integral \\( \\int_{-1}^{-2}\\int_{-1}^{-2}\\int_{-1}^{-2}\\frac{x^2}{x^2+y^2+z^2}dxdydz \\).",
"role": "user"
}
] | \dfrac{1}{3} |
[
{
"content": "Determine the order of growth of the complex polynomial \\( p(z) = a_nz^n + \\ldots + a_1z + a_0 \\).",
"role": "user"
}
] | 0 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1750 m |
[
{
"content": "Determine the interval of convergence for the integral \\( \\int_0^1 \\frac{x^p}{1-x} \\, dx \\).",
"role": "user"
}
] | \emptyset |
[
{
"content": "Find the range of the expression \\( \\left[ f(x) - \\frac{1}{2} \\right] + \\left[ f(-x) - \\frac{1}{2} \\right] \\), where \\( f(x) = \\frac{a^x}{1 + a^x} \\) with \\( a > 0 \\) and \\( a \\neq 1 \\), and \\([m]\\) denotes the greatest integer less than or equal to \\( m \\).",
"role": "user... | \{-1, 0\} |
[
{
"content": "Let $f(z)$ be an entire function that is real on the real axis, with $f(0) = 1$. Assume there exists a real constant $M$ such that $|f(z)| \\le M$ for all $z$ with $\\text{Im}(z) \\ge 0$. Evaluate \\( \\lim\\limits_{x \\rightarrow + \\infty}{f(x)}. \\)",
"role": "user"
}
] | 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 5.73e-2 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 1450 N |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | 4.69 atm |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | x(t) = 4(t^4/108 + t^3 + 9t^2/2) - t + 1 |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | length, mass, and tension of the string |
[
{
"content": "Two transformations are applied to the complex number $-3 - 8i$:\n\nA $45^\\circ$ rotation around the origin in the counter-clockwise direction.\nA dilation, centered at the origin, with scale factor $\\sqrt{2}.$\n\nWhat is the resulting complex number?",
"role": "user"
}
] | 5 - 11i |
[
{
"content": "A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer. The reasoning process and answer are enclosed within <think> </think> and <answer> </answ... | O(C^2N) |
[
{
"content": "In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is 15. What is the greatest possible perimeter of the triangle?",
"role": "user"
}
] | 43 |
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