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I have made up the sentences below.

(1) I want to exchange my colorful postage stamp with you for your diamond-shaped one.

(2) I want to trade my colorful postage stamp with you for your diamond-shaped one.

Most of my non-native English speaking friends think I'm using the two verbs correctly. However, a few of my other friends think disagree with them.

What is your opinion? Thank you very much.

+1

You could also say

eg I want to swap my colorful postage stamp for your diamond-shaped one.

+0

They both sound OK to me.