This is an issue with typeshed due to a limitation in the type system. foo can return either an int or a float, depending on whether x is a positive or negative number. While we could change typeshed in a way that 2 ** x will always return float (which is correct, since for typing purposes int is a subtype if float), this would be rather annoying for users that know that it will return an int, for example because they know that x is always non-negative. Therefore we return Any, because there is no way to properly express this.

We would need a range type to be able to express this.

Wouldn't Union[int, float] be a better option instead of Any? The users can then assert that the result is an int if they are sure that x is non-negative.

Also, a related problem is that

def foo(x: int) -> float:
    return 2 ** x

fails with mypy --strict. What is the recomended way to deal with this? Explicit type conversion (float(2 ** x))?

Wouldn't Union[int, float] be a better option instead of Any? The users can then assert that the result is an int if they are sure that x is non-negative.

We try to avoid that sort of union return in typeshed stubs because they produce a pretty bad user experience.

Also, a related problem is that

def foo(x: int) -> float:
    return 2 ** x

fails with mypy --strict. What is the recomended way to deal with this? Explicit type conversion (float(2 ** x))?

Yeah, probably. --disallow-return-any maybe shouldn't be in --strict? See #7767 which I just opened