'Eager' in the Bible

That is why I am so eager to proclaim the gospel to you who live in Rome, too.

because the believers in Macedonia and Achaia have been eager to share their resources with the poor among the saints in Jerusalem.

Yes, they were eager to do this, and in fact they are obligated to help them, for if the gentiles have shared in their spiritual blessings, they are obligated to be of service to them in material things.