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Hmm, I don't know much about verbatim or defining new variables. You are right about fragility, though, I get that kind of thing in beamer a lot. What I would do is this.
\begin{sagesilent}
## Boring computation
## final result x = my_result
\end{sagesilent}
%% Lotsa discussion
\appendix
The answer is $\sage{x}$.
Probably this should work?
