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Ah yes, I have always mixed these words!

Yes right, nobody says "Я нуждаюсь в ручке" - only the German SS officers in Soviet movies when they are invited to write the confession after being promised to be executed gently.

Мне нужна ручка...

нуждаться - to need
требовать - to demand

The common and polite form of demanding anything is to ask that:

Would you hand me a pen, please?- не подадите ли мне ручку?
Give me a pen, please. -...