The Any return type is intentional here because Union return types are generally annoying to deal with. This is mentioned in https://github.com/python/typeshed/blob/master/CONTRIBUTING.md#conventions.

I don't really agree with that as the user always has the option to cast or just ignore Union return types and having specific types is the purpose of stub files but sorry for the fuss if it's common convention.

Then again, that convention is not followed consistently. There are e.g. signatures for next and sum in the same file that do have Union return types...

The union return types for next() and sum() are only overloads for special cases, and in most cases the union will disappear because the iterator item type and the default/start value type are the same.

There's absolutely no requirement for isinstance. Other options the user has include:

• cast(int, n**2) when we know that the result will be int
• cast(Any, n**e) or n**e # type: ignore when we don't want to deal with the type (why use types at all then?)
• float(n**e) when both types are possible and we do not want to distinguish

All of those have the same problem as isinstance -- if you have working correct code, mypy gives you a false positive forcing you to make it uglier. While sometimes that's the right thing to do (e.g. a = []), usually we prefer false negatives over false positives, since false positives very quickly annoy users. Remember that mypy users are Python users first and foremost, not type system zealots. :-)

By the way, mypy already special cases type checking of n**m for integers when m is a literal, and it can infer int / float as the type instead of Any.