"...as you have believed, so let it be done for you." When the centurion heard this he fully expected that what he requested Jesus to do is exactly what Jesus would do! He believed Jesus would heal his servant and that's what happened.
God wants to be believed! When we pray we're told by James, "But let him ask in faith, with no doubting..." James 1:6. The centurion didn't doubt. He received what he believed Jesus would do.
When the Bible tells us what God is willing to do for us, such as James 1:5, "If any of you lacks wisdom, let him ask of God, who gives to all liberally and without reproach, and it will be given him", then God means what He said! We should pray in faith and expect God to answer.
He said it. He means it. He will do it! Believe Him.