Note: It's possible that in the future, Wolfram Alpha will improve and be able to answer the questions in this answer, so it's best to actually try them in Wolfram Alpha first.
Use questions that involve conditional statements and generic expressions.
For example:
If $\lim_{x\to\infty} f(x)=1$, then what is $\lim_{x\to\infty}\frac{f(x)}{x}$ equal to?
Typing limit of (f(x)/x) as x goes to infinity if limit of f(x) as x goes to infinity is equal to 1
or limit of f(x) as x goes to infinity is equal to 1, what is limit of f(x)/x as x goes to infinity?
or if limit of f(x) as x goes to infinity is equal to 1, then what is limit of f(x)/x as x goes to infinity?
into Wolfram Alpha doesn't give the answer.
A more difficult one:
If $\lim_{x\to\infty} f(x)=1$, then what is $\lim_{x\to\infty}\frac{x-f(x)}{x+f(x)}$ equal to?
One involving derivatives:
If $f'(x)=\sqrt{x}\cos(\pi x^2)$, then what is $f'(4)$?
(Intentionally choose $f(x)=\int\sqrt{x}\cos(\pi x^2)\,\mathrm{d}x$ to be ridiculously complicated.) Typing If f'(x)=x^0.5cos(pi x^2), then what is f'(4)?
into Wolfram Alpha doesn't work.
Make it clear to the students that $f'(4)$ (which is $2$), is not the same as $\frac{\mathrm{d}}{\mathrm{d}x}\left(f(4)\right)$ (which is $0$).
You can then ask (after discussing the chain rule) the more difficult question:
If $f'(x)=\sqrt{x}\cos(\pi x^2)$, then what is $\frac{\mathrm{d}}{\mathrm{d}x}\left(f(x^2)\right)$?