'Supplication' in the Bible

Then these men assembled, and found Daniel praying and making supplication before his God.

"So I turned my attention to the Lord God, seeking him in prayer and supplication, accompanied with fasting, sackcloth, and ashes.

and now, hearken, O our God, unto the prayer of Thy servant, and unto his supplication, and cause Thy face to shine on Thy sanctuary that is desolate, for the Lord's sake.

And whiles I was speaking, and praying, and confessing my sin and the sin of my people Israel, and presenting my supplication before the LORD my God for the holy mountain of my God;