What is the ruling of Islamic law on borrowing a sum of money with interest from a bank, then wishing not to pay the interest after learning of the prohibition of usury, and what is the ruling on a friend providing a free service to the bank equivalent to the value of that interest?

Praise Allah for enlightening you about the impermissibility of this usurious transaction. Repent to Allah with sincere repentance. If it is possible to waive this interest, then that is what must be done, for Allah Almighty says: "But if you repent, you may have your principal – [thus] you do no wrong, nor are you wronged." If it is not possible to waive it, then pay it, and your sincere repentance will suffice you. As for the second part, it is not permissible for your friend to cooperate with the usurious bank due to the cooperation in sin and aggression involved. However, if the service he provides cancels the interest, then there is no harm, provided its harm does not exceed the harm of paying the interest.