Run Examples in CI

[tjlaboss]

Is your feature request related to a problem? Please describe.
Example code is not tested automatically. It can fall out of date without anyone noticing, or it might not run out of the box.

Describe the solution you'd like
During CI, add an example-test that at least makes sure that the examples and demos execute.

Additional context
In #571, a demo does run without manual intervention.

In #559, @MicahGale suggests adding doctest, which is relevant.

[MicahGale]

So what's the scope?

1. README.md
2. /doc
3. /demo?

Also most examples are pseudo-code, so this will take a little bit of effort to implement.