Inheriting from built-in types

I'd like to create a new type which is polymorphic to int but has some
different characteristics, something like this:

struct ModuloInt : int {                          // <-- Note: class
derives from int
    ModuloInt(int Value) : int(Value) {};
    };

int main(void) {

    ModuloInt i = 10;
    }

Neither Microsoft C++ 2008 (Express) nor gcc version 4.1 thinks this
is legal. I've looked all over the net, but no one has an example of
this or explains why this type of inheritance won't work.

I can of course make the new class by composition and operator
overloading, but I always thought that the builtin types were
considered classes in C++.

Is there a rule somewhere which states that only user-defined classes
can be inherited from?