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The below should probably say something along the lines of "max expected 1 positional arguments" (since the foo value is an argument):
>>> max(foo=1)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
TypeError: max expected 1 arguments, got 0
I imagine this affects other functions, but I haven't looked into which ones.
Here is an example of another built-in function that provides a better message:
>>> sorted(foo=1)
Traceback (most recent call last):
 File "<stdin>", line 1, in <module>
TypeError: Required argument 'iterable' (pos 1) not found

It would be nice to change 'arguments' to 'argument' in this case, too. :-)

Attached an initial patch:
>>> max()
TypeError: max() requires at least a positional argument
>>> max(foo=3)
TypeError: max() requires at least a positional argument
>>> max(3, foo=3)
TypeError: max() got an unexpected keyword argument
>>> max(3, 4)
4

Would it make sense to adjust the error messages in PyArg_UnpackTuple instead? I suspect there are quite a lot of functions using it.

PyArg_UnpackTuple could be fixed to say "positional argument" (see attached patch (maybe this should be a separate issue)).
The error returned by max() is wrong because PyArg_UnpackTuple is used on the *args alone first, and it has no knowledge of the kwargs.
If PyArg_UnpackTuple is used to parse the *args then adding "positional" should solve the problem, however for this specific case the error would still be incorrect, because max also accepts more positional args.

Yes, true: max is probably still going to have to be a special case, thanks to its schizophrenic signature. (max([1, 2, 3]) versus max(1, 2, 3)).

I created #16543 for PyArg_UnpackTuple.
Once that is fixed we can continue with this.