The line: virtual double function \( X() \) const \( =0 \); in a class definition indicates that the class is probably a: Base class. Library class. Protected class. Derived class.

This line indicates that the class is a base class, specifically an abstract base class. When a class contains at least one pure virtual function (like the one you've shown with \( =0 \)), it cannot be instantiated directly. Instead, it's intended to be a blueprint for derived classes that must implement the pure virtual function to provide specific functionality. It's like an artist providing a canvas where different painters can create their unique masterpieces! In practical terms, using abstract base classes encourages a design that relies on polymorphism, enhancing the flexibility and scalability of your code. For instance, if you have a base class `Shape`, derived classes like `Circle`, `Square`, or `Triangle` can implement the `X` function to calculate their respective areas. This allows your program to handle various shapes uniformly, making it robust and versatile in real-world applications!