Add Code Examples in Docstrings to CI Workflows

[Kleinjohann]

While implementing #800 I noticed some examples in function docstrings were not changed when the API of those functions changed. Currently examples in docstrings seem not to be tested at all. Maybe there's a way to add them to the CI workflows? Any thoughts?

[apdavison]

The doctest library could be used for this.

I don't think this is a high priority, but we'd be happy to have someone work on this.