solution: We can perform long division.  Alternatively, by the Remainder Theorem, the remainder upon division is $(-1)^6 - 3 = -2.$  Thus, we can write
  \begin{align*}
  \frac{x^6 - 3}{x + 1} &= \frac{(x^6 - 1) - 2}{x + 1} \\
  &= \frac{x^6 - 1}{x + 1} - \frac{2}{x + 1} \\
  &= \frac{(x^3 - 1)(x^3 + 1)}{x + 1} - \frac{2}{x + 1} \\
  &= \frac{(x^3 - 1)(x + 1)(x^2 - x + 1)}{x + 1} - \frac{2}{x + 1} \\
  &= (x^3 - 1)(x^2 - x + 1) - \frac{2}{x + 1} \\
  &= x^5 - x^4 + x^3 - x^2 + x - 1 - \frac{2}{x + 1}.
  \end{align*}Thus, the quotient is $\boxed{x^5 - x^4 + x^3 - x^2 + x - 1}.$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Find the quotient when $x^6 - 3$ 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^5 - x^4 + x^3 - x^2 + x - 1
extra_info.question: Find the quotient when $x^6 - 3$ is divided by $x + 1.$
extra_info.split: test