solution: We can write
  \begin{align*}
  \sin^3 18^\circ + \sin^2 18^\circ &= \sin^2 18^\circ (\sin 18^\circ + 1) \\
  &= \sin^2 18^\circ (\sin 18^\circ + \sin 90^\circ).
  \end{align*}By sum-to-product,
  \begin{align*}
  \sin^2 18^\circ (\sin 18^\circ + \sin 90^\circ) &= \sin^2 18^\circ \cdot 2 \sin 54^\circ \cos 36^\circ \\
  &= 2 \sin^2 18^\circ \cos^2 36^\circ \\
  &= \frac{2 \sin^2 18^\circ \cos^2 18^\circ \cos^2 36^\circ}{\cos^2 18^\circ} \\
  &= \frac{4 \sin^2 18^\circ \cos^2 18^\circ \cos^2 36^\circ}{2 \cos^2 18^\circ}.
  \end{align*}Then by double angle formula,
  \begin{align*}
  \frac{4 \sin^2 18^\circ \cos^2 18^\circ \cos^2 36^\circ}{2 \cos^2 18^\circ} &= \frac{\sin^2 36^\circ \cos^2 36^\circ}{2 \cos^2 18^\circ} \\
  &= \frac{4 \sin^2 36^\circ \cos^2 36^\circ}{8 \cos^2 18^\circ} \\
  &= \frac{\sin^2 72^\circ}{8 \cos^2 18^\circ} \\
  &= \boxed{\frac{1}{8}}.
  \end{align*}Alternatively, we can plug in the value $\sin 18^\circ = \frac{\sqrt{5} - 1}{4}.$
prompt.content: <|im_start|>system
  You are a helpful assistant.<|im_end|>
  <|im_start|>user
  Compute $\sin^3 18^\circ + \sin^2 18^\circ.$
  Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
  <|im_start|>assistant
  
prompt.role: user
extra_info.answer: \frac{1}{8}
extra_info.question: Compute $\sin^3 18^\circ + \sin^2 18^\circ.$
extra_info.split: test