Can I be asked by an undercover officer to expose my self to him, then be arrested for indecent exposure while in a secluded place?

That sounds like entrapment. I would need to get all the details first though.

Sure. You were free to decline to do that, and you chose to do it. Having exposed yourself, you were then subject to arrest if you were in a public location, even if you felt you were somewhat secluded. You did not know at the time you were exposing yourself to a law enforcement officer. You thought you were doing so to a member of the general public.

It is not the fact that you exposed yourself to the officer, but you were reckless about whether others would see you and be offended. This is a typical sting cops pull.