in reply to
Perl module symbol import versus direct invocation
Actually, it does. Calling a function using the -> syntax calls it as an object method. The only practical distinction is that the first argument passed to the function then becomes a reference to the object (it is supplied automatically by Perl as part of the -> magic). This is probably the source of your error (though I can't be sure, not having seen the source of Date::Calc).
Try instanstiating a Date::Calc object before calling Add_Delta_Days with -> .
Update: You seem to be confusing fully qualifying a symbol with object calling syntax. What you want to do when you qualify a symbol with the package name is Date::Calc::Add_Delta_Days.