solution: We can perform long division.  We can also write
  \begin{align*}
  \frac{x^9 + 1}{x - 1} &= \frac{(x^9 - 1) + 2}{x - 1} \\
  &= \frac{x^9 - 1}{x - 1} + \frac{2}{x - 1} \\
  &= x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 + \frac{2}{x - 1}.
  \end{align*}Thus, the quotient is $\boxed{x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1}.$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Find the quotient when $x^9 + 1$ is divided by $x - 1.$
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1
extra_info.question: Find the quotient when $x^9 + 1$ is divided by $x - 1.$
extra_info.split: test