Can we say "There should be any problem for Adam to eat that apple"? [closed]
No, it's not a proper sentence.
Any in this sense is a negative polarity item, and therefore can't appear outside a negative context.
Thus, while
- There shouldn't be any problem for Adam to eat that apple
is OK, because shouldn't is negative,
- *There should be any problem for Adam to eat that apple
is ungrammatical because should isn't negative.