prompt list | ground_truth string |
|---|---|
[
{
"content": "In an arbitrary metric space $(X,d)$, let $A$ be a subset of $X$. Determine whether it is always true that $\\mathrm{int}(A \\setminus \\mathrm{int}(A)) = \\emptyset$. Provide a justification for your answer.",
"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... | 4.5 kg.m/s |
[
{
"content": "A stick 5 cm long, a stick 9 cm long, and a third stick $n$ cm long form a triangle. What is the sum of all possible whole number values of $n$?",
"role": "user"
}
] | 81 |
[
{
"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... | 0.167 |
[
{
"content": "Evaluate \\( \\lim _{n\\to \\infty }\\int _{0}^{1}nx^ne^{x^2}dx \\).",
"role": "user"
}
] | e |
[
{
"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... | 0.19 V |
[
{
"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... | 0.94 cm |
[
{
"content": "Let $\\delta$ be a smooth function on $(0,\\infty)$ such that: (i)$\\lim\\limits_{s\\to\\infty}\\delta(s)=0$, (ii)$\\lim\\limits_{s\\to\\infty}s\\delta^\\prime(s)=0$. Additionally, $\\lim\\limits_{s\\to\\infty} s^m\\delta^{(m)}(s)=0$ for any $m\\in\\mathbb{N}$. Suppose there exist $s_0>1$ and $M>0... | Yes |
[
{
"content": "For which positive integer values of $k$ does $kx^2+20x+k=0$ have rational solutions? Express your answers separated by commas and in increasing order.",
"role": "user"
}
] | 6, 8\text{, and }10 |
[
{
"content": "Find a space that is homeomorphic to the quotient space $\\mathbb{R}^3 / \\sim$, where the equivalence relation $\\sim$ is defined by $(x, y, z) \\sim (x, y', z')$ for any $y', z' \\in \\mathbb{R}$.",
"role": "user"
}
] | \mathbb{R} |
[
{
"content": "Determine whether there exists an infinite Hausdorff space \\((X, \\tau)\\) such that for every proper equivalence relation \\(\\vartheta\\) on \\(X\\), the space \\(X\\) is not homeomorphic to the quotient space \\(X/\\vartheta\\).",
"role": "user"
}
] | Yes |
[
{
"content": "Let \\( P(x) \\) be a polynomial function such that \\( P(x^2) = x^2(x^2+1) P(x) \\) and \\( P(2) = 3 \\). Find \\( P(3) \\).",
"role": "user"
}
] | 18 |
[
{
"content": "Find the probability that the length of a randomly chosen chord of a circle lies between \\(\\frac{2}{3}\\) and \\(\\frac{5}{6}\\) of its diameter.",
"role": "user"
}
] | \dfrac{1}{4} |
[
{
"content": "Calculate the integral \\(\\iiint\\limits_{\\mathbb{R}^3}{\\frac{5\\cdot e^ {- 4\\cdot \\left(z^2+y^2+x^2\\right) }}{\\sqrt{z^2+y^2+x^2}}}\\,\\mathrm{d}V\\) in spherical coordinates, where \\((x, y, z) \\mapsto (\\rho\\cos\\theta\\sin\\phi, \\rho\\sin\\theta\\sin\\phi, \\rho\\cos\\phi)\\) and \\(\... | \dfrac{5\pi}{2} |
[
{
"content": "Find the last two digits of the number \\( n = 2017^{(2018)^{(2019)^{(\\cdots)}}} \\).",
"role": "user"
}
] | 41 |
[
{
"content": "Determine the units digit of the series \\(2^{2^2}+4^{4^4}+6^{6^6}+\\cdots+2016^{2016^{2016}}+2018^{2018^{2018}}\\) without individually computing each term.",
"role": "user"
}
] | 8 |
[
{
"content": "Find the splitting field of the polynomial \\( P(X) = X^4 + 1 \\) over \\( \\mathbb{Q} \\) and determine the degree of this field over \\( \\mathbb{Q} \\).",
"role": "user"
}
] | 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... | Switchgrass is economically favorable to cultivate and produce, its cost of production is much less compared to the amount of energy produced, and its cultivation would solve the problem of soil erosion. |
[
{
"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... | 154.029 kmph |
[
{
"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... | I_2 |
[
{
"content": "Determine the values of \\( \\beta \\) for which the integral \\( \\int_{1}^{+ \\infty} \\left(\\frac{1}{\\sqrt{x^2 + 2x + 2} + x + 1}\\right)^\\beta \\, dx \\) converges.",
"role": "user"
}
] | \beta > 1 |
[
{
"content": "Let $n$ equal the number of sides in a regular polygon. For $3\\leq n < 10$, how many values of $n$ result in a regular polygon where the common degree measure of the interior angles is not an integer?",
"role": "user"
}
] | 1 |
[
{
"content": "Evaluate the limit \\(\\lim_{(x,y)\\to (0,0)} \\frac {\\sin(y^2-xy)}{\\vert y\\vert}\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Can a conditionally convergent series be rearranged to converge to a different value?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine the space complexity of storing bit string representations of the numbers in the factorial sequence.",
"role": "user"
}
] | O(n^2 \log 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... | 40.9 m/s |
[
{
"content": "Given the recurrence relation $a_{n+1} = \\frac{10}{a_n} - 3$ with the initial condition $a_1 = 10$, find $\\lim_{n \\to \\infty} a_n$. \\(\\text{(Express your answer as a single number or expression.)}\\)",
"role": "user"
}
] | -5 |
[
{
"content": "Are there any known perfect numbers that do not have the form \\((2^p-1)\\cdot 2^{p-1}\\) where \\(2^p-1\\) is prime?",
"role": "user"
}
] | No |
[
{
"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... | 3.77 A |
[
{
"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... | 9.702e12 W |
[
{
"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... | {eq}- \frac{1}{2}\frac{{d\left[ {\rm{A}} \right]}}{{dt}} = \frac{{d\left[ {\rm{P}} \right]}}{{dt}}{/eq} |
[
{
"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... | 2.07 m/s at 23.79 degrees east of south |
[
{
"content": "Can Elector Georg determine which of his 100 coins are counterfeit by consulting an expert fewer than 120 times, given that the expert always exaggerates the number of counterfeit coins by a fixed unknown natural number?",
"role": "user"
}
] | Yes |
[
{
"content": "Determine whether there exists a multiple of \\(5^{100}\\) that does not contain the digit 0 in its decimal representation.",
"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... | 3.988A |
[
{
"content": "Determine whether the statement is true or false: If $p$ is a prime number, then $(p)$ is a prime ideal in $\\mathbb{Z}[x,y]$. Provide a justification for your answer.",
"role": "user"
}
] | A |
[
{
"content": "Consider the set \\(S = \\mathbb{R} \\times \\mathbb{C}\\). For elements \\(a = (x_a, z_a)\\) and \\(b = (x_b, z_b)\\) in \\(S\\), define the binary operation \\(\\circ\\) as:\n\\[ a \\circ b = (x_a + x_b, x_a + ix_b + z_a + z_b) \\]\nwhere \\(i\\) is the imaginary unit with \\(i^2 = -1\\). We say... | B |
[
{
"content": "Carpet costs $\\$21.95$ per square yard and the padding to put under it costs $\\$2.55$ per square yard. Felix plans to install padding and carpet in the region shown in the diagram. What is the cost of the carpet and padding needed to exactly cover the room?\n\n[asy]\nunitsize(0.2 inch);\n//impor... | 735 |
[
{
"content": "In a regular tetrahedron \\(ABCD\\), point \\(E\\) is on edge \\(AB\\) and point \\(F\\) is on edge \\(CD\\) such that \\(\\frac{AE}{EB} = \\frac{CF}{FD} = \\lambda\\), where \\(0 < \\lambda < +\\infty\\). Define \\(f(\\lambda) = \\alpha_{\\lambda} + \\beta_{\\lambda}\\), where \\(\\alpha_{\\lambd... | D |
[
{
"content": "Compute the integral \\( \\int_{-\\infty}^{\\infty} [F(x+10) - F(x)] \\, dx \\), where \\( F \\) is a distribution function.",
"role": "user"
}
] | 10 |
[
{
"content": "Consider the vector space $\\mathbb{P}_2(\\mathbb{R})$ of real polynomials with degree 2 or lower. Define the linear operator $T: \\mathbb{P}_2(\\mathbb{R}) \\rightarrow \\mathbb{P}_2(\\mathbb{R})$ by $T(f(x)) = f''(x) + f'(x) + f(0)x^2$. Given the vector $g(x) = x$, determine the characteristic p... | -t^3 + 2t + 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... | mental health |
[
{
"content": "Given positive real numbers $x$ and $y$ such that $\\log_y x + \\log_x y = 7$, what is $(\\log_y x)^2 + (\\log_x y)^2$?",
"role": "user"
}
] | 47 |
[
{
"content": "Given that \\(\\operatorname{tg} \\alpha\\) and \\(\\operatorname{tg} \\beta\\) are the roots of the equation \\(x^{2} + px + q = 0\\), find the value of the expression:\n\\[ \\sin^{2}(\\alpha + \\beta) + p \\sin(\\alpha + \\beta) \\cos(\\alpha + \\beta) + q \\cos^{2}(\\alpha + \\beta). \\]",
... | q |
[
{
"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... | 131 g of S8 |
[
{
"content": "Evaluate the infinite series: $$\\sum_{k=1}^\\infty \\frac{(-1)^{k-1}}{k}\\sum_{n=0}^\\infty \\frac{1}{k2^n+1}.$$",
"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... | 6675 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... | 11.196 eV |
[
{
"content": "Evaluate the double integral \\( \\iint_D \\frac{xy}{\\sqrt{1-y^2}} \\, dx \\, dy \\), where \\( D \\) is the region in the first quadrant bounded by the unit circle \\( x^2 + y^2 = 1 \\).",
"role": "user"
}
] | \dfrac{1}{6} |
[
{
"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... | 147706 |
[
{
"content": "Find the last three digits of the sum \\( S = \\sum_{i=2}^{10^7} (i^7 + i^5) \\).",
"role": "user"
}
] | 998 |
[
{
"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... | y=\frac{d \ tan\theta \ tan\phi}{tan\phi-tan\theta} |
[
{
"content": "Determine a generator of the multiplicative group \\( \\mathbb{Z}^{*}_{242} \\).",
"role": "user"
}
] | 7 |
[
{
"content": "Determine the number of non-isomorphic quotient groups of the symmetric group $S_4$.",
"role": "user"
}
] | 4 |
[
{
"content": "Evaluate the limit: \\[ \\lim_{n\\to\\infty} \\left(\\frac{n!}{n^n}\\right)^{1/n} \\]",
"role": "user"
}
] | \dfrac{1}{e} |
[
{
"content": "Let \\(p \\ge 1\\) and \\(A \\in \\mathcal{B}(\\mathbb{R})\\). Assume that \\(N := \\overline{A} \\setminus A\\) is a Lebesgue null set. Can any function \\(f \\in \\mathcal{L}^p(A)\\) be extended to a function \\(g \\in \\mathcal{L}^p(\\overline{A})\\)? Justify your answer.",
"role": "user"
... | Yes |
[
{
"content": "If $e^{i \\theta} = \\frac{2 + i \\sqrt{5}}{3},$ then find $\\sin 4 \\theta.$",
"role": "user"
}
] | -\frac{8 \sqrt{5}}{81} |
[
{
"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... | 82.0 mT |
[
{
"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... | 127250 |
[
{
"content": "Determine the minimum value of the function \\( f(x) = \\frac{\\cos^3(x)}{\\sin(x)} + \\frac{\\sin^3(x)}{\\cos(x)} \\) on the interval \\( (0, \\pi/2) \\).",
"role": "user"
}
] | 1 |
[
{
"content": "In triangle $\\triangle ABC$, it is given that $\\frac{\\sin B}{\\sin C} = \\frac{3}{4}$ and $\\frac{\\sin C}{\\sin A} = \\frac{5}{6}$. Determine the value of $\\frac{|AB| \\cdot |BC|}{|AC|}$.",
"role": "user"
}
] | 32 |
[
{
"content": "Let $f: \\mathbb{D} \\to \\widehat{\\mathbb{C}}$ be a meromorphic function inside the unit disk. Assume that $f$ is zero on the boundary and continuous in the closed disk (as a function into $\\widehat{\\mathbb{C}}$). Is $f$ necessarily identically zero?",
"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... | The beginning energy level is n=2, and the ending energy level is n=5. |
[
{
"content": "Determine the smallest integer $k$ such that the following conditions are satisfied for 14 students at the IMO training camp: (a) The students can be arranged in a circle such that every two adjacent students have different favorite numbers. (b) Among the students, 7 are boys and the rest are girl... | 2 |
[
{
"content": "Determine the type of singularity and compute the residue of the function \\( \\frac{1}{\\sin^2(z)} \\) at \\( z = 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... | 52.02 m |
[
{
"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... | 641 mph |
[
{
"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... | 1.43L |
[
{
"content": "What is the product of $0.\\overline{05}$ and $1.8$ expressed as a fraction in simplest form?",
"role": "user"
}
] | \frac{1}{11} |
[
{
"content": "Evaluate the infinite series: \\[ \\sum_{n=1}^{\\infty} \\frac{2^n}{n(n+2)} \\cdot \\frac{5n+18}{3^n} \\]",
"role": "user"
}
] | 8 |
[
{
"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... | 1.70e-6 H/m |
[
{
"content": "Determine the smallest dimension $n$ for which there exists a closed oriented $n$-manifold whose homology groups are isomorphic to any given sequence of finitely generated abelian groups $G_1, \\dots, G_{2m+1}$, where $m$ is a positive integer.",
"role": "user"
}
] | 4m + 3 |
[
{
"content": "For any integer \\(n > 2\\), determine if there exist positive integers \\(m\\) and a real number \\(q\\) in the interval \\((1,2)\\) such that the inequality \\(q^{n-1}(q-1)+1 \\le q^m\\) holds.",
"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... | 240 |
[
{
"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... | 26.6% |
[
{
"content": "A library has six identical copies of a certain book. At any given time, some of these copies are at the library and some are checked out. How many different ways are there for some of the books to be in the library and the rest to be checked out if at least one book is in the library and at least... | 5 |
[
{
"content": "Let \\((a_n)_n\\) be a convergent sequence. Determine \\(\\lim_{n \\to \\infty} n \\Delta(a_{n+1}) = \\lim_{n \\to \\infty} n (a_{n+1} - a_n)\\).",
"role": "user"
}
] | 0 |
[
{
"content": "Evaluate the limit \\( \\lim_{x\\rightarrow 0}\\frac{f(x)}{x^{8}} \\), where \\( f(x)=\\int_{0}^{x^{4}}e^{\\sqrt t }\\cdot\\sin t \\ dt \\).",
"role": "user"
}
] | \dfrac{1}{2} |
[
{
"content": "Given an element $b$ of a $C^*$-algebra $B$ that is self-adjoint and satisfies $\\|b-b^2\\|<1$, determine if there exists a projection $p \\in B$ such that $\\|b-p\\|<2$. Provide a justification for your conclusion.",
"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... | 3.2% |
[
{
"content": "A circle with center $C$ is tangent to the positive $x$ and $y$-axes and externally tangent to the circle centered at $(3,0)$ with radius $1$. What is the sum of all possible radii of the circle with center $C$?",
"role": "user"
}
] | 8 |
[
{
"content": "Calculate the work done by the engine pistons during a four-stroke cycle when the pressure is described by the vector field \\( P = (y - x^2)\\mathbf{i} + (z - y^2)\\mathbf{j} + (x - z^2)\\mathbf{k} \\), and the volume curve is \\( V(t) = t\\mathbf{i} + t^2\\mathbf{j} + t^3\\mathbf{k} \\), from \\... | \dfrac{29}{60} |
[
{
"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... | $7,857.14 |
[
{
"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... | 150.8Nm |
[
{
"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... | Cost of goods sold: 125
Purchases: 75
Inventory: 50 |
[
{
"content": "Determine the range of the function \\( f(x)=\\sqrt{36-g^2(x)} \\), where \\( g(x) = -8 - 2 \\cos 8x - 4 \\cos 4x \\).",
"role": "user"
}
] | [0, \sqrt{11}] |
[
{
"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... | 0.565 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... | 2.1*10^3 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... | 28195 |
[
{
"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... | 25.03 m |
[
{
"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... | Major depressive disorder |
[
{
"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... | $251.53 |
[
{
"content": "Calculate the flux of the vector field \\( v = (yz, y^2z, yz^2) \\) through the surface of the cylinder defined by \\( x^2 + y^2 = 1 \\) and \\( 0 \\leq z \\leq 1 \\). Use the divergence theorem to simplify your calculations.",
"role": "user"
}
] | 0 |
[
{
"content": "Find the closure of the set \\( \\{ \\frac{1}{2} \\} \\) in the topology generated by the basis \\( B = \\{ (n, n+1) : n \\in \\mathbb{Z} \\} \\cup \\{ \\{ k \\} : k \\in \\mathbb{Z} \\} \\).",
"role": "user"
}
] | (0, 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... | -50 degrees |
[
{
"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... | 8.448 g |
[
{
"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... | Ghana, Ivory Coast, Senegal, and Benin have seen significant economic growth due to poverty eradication efforts and revenue from mineral extraction. |
[
{
"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... | rope wave, infrared, red light, low-frequency x-rays, high-frequency x-rays, gamma-ray radiation |
[
{
"content": "Determine whether the following statement is true or false: For any continuous function $g$ on an interval $(p,q)$ and $d\\in(p,q)$, there exist points $y_1,y_2\\in(p,q)$ such that $\\frac{g(y_2)-g(y_1)}{y_2-y_1}=g'(d)$.",
"role": "user"
}
] | B |
[
{
"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... | 1028.81 |
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