Question

_ you mind giving me your pen for a minute.(should,would,could)​

Answer 1

Answer:

would

Explanation:

you mind giving me your pen for a minute

Answer 2

Answer:

Would you mind to giving me your pen for a minute.

Because

Would is used to ask polite questions.

Example

Would you like a cup of coffee? (More polite than ‘Will you like a cup of coffee?’)

Would you mind lending me your bicycle?