[David L.]

The teacher has been trained to teach us well.

(He was educated before he then undertook teacher training, and probably will continue to learn (further his education, perhaps by private reading.)

You are right. He was trained to become a teacher (a completed action in the past) but we presume that he is now engaged in teaching, which links the past completed action with the present, right up to now, so we would use present perfect tense.
The choice of tense has little to do with 'teach us well'. For examples:

The teacher was trained to teach us well, but he has become an alcoholic and is so hung-over in class, he just tells us to read our text books.


The teacher has been trained to teach us well but he has had so much time off work that we are way behind in our curriculum.

As I recall my chemistry and electrolysis, and anodes and cathodes :
I didn't ask you whether copper is positively or negatively loaded.


...or
'I would appreciate any help you can give."