in the book UML @ Classroom An Introduction to Object-Oriented Modeling is written "Use cases—even included or extending use cases—can always be executed independently. If they can only be executed within the scope of another use case and not independently, they are not use cases and must not be depicted as such. Their functionality must then be covered in the description of the use case that uses them.", however all examples of extends relationships my Professor gave to me and I found in internet the extending use cases can only be triggered within the scope of the base use case. I'm lost, which one is correct ?
I have a mini-project, I ignored the extending use cases that can't be triggered by any actor, should I draw these extending use cases ?
The independence is a practical way to avoid functional decomposition. Considering that functional decomposition is not a bad use-case practice (even if UML specs explicitly allow it), it is a good idea to look for independent use-cases.
Extensions should also follow this rule, but not for the reason you think. By definition, the extension is an additional behavior that makes sense only in the context of the extended use-case:
It is therefore very difficult to have an independent extensiin. Nevertheless, still you shoukd apply the rule of your book: avoid dependent use-cases. Therefore avoid extensions at all. And this is good, because most often extznsions present something very detailed that could as well be explained in the narrative of the extended use-case ;-)