For our first example, I have selected a relatively short prayer (2 Kings 19:15-19). As we go through other prayers notice they differ in the length and depth of the first 2 phases, but they all reference justice and ask God for a value.
“And Hezekiah prayed before the LORD, and said, O LORD God of Israel, which dwellest between the cherubims, thou art the God, even thou alone, of all the kingdoms of the earth: thou hast made heaven and earth.
LORD, bow down thine ear, and hear: open, LORD, thine eyes, and see: and hear the words of Sennacherib, which hath sent him to reproach the living God.
Of a truth, LORD, the kings of Assyria have destroyed the nations and their lands, And have cast their gods into the fire: for they were no gods, but the work of men's hands, wood and stone: therefore they have destroyed them.
Now therefore, O LORD our God, I beseech thee, save thou us out of his hand, that all the kingdoms of the earth may know that thou art the LORD God, even thou only.”
The first sentence actually contains the first two phases of the prayer. The first sentence consists of Hezekiah recognizing God (O LORD God of Israel) and praising Him as the God of all the kingdoms (which dwellest between the cherubims, thou art the God, even thou alone, of all the kingdoms of the earth).
Hezekiah builds his faith through knowledge by recognizing that God made heaven and earth. (thou hast made heaven and earth)
The second sentence makes a request of God to hear the words of Sennacherib (LORD, bow down thine ear, and hear: open, LORD, thine eyes, and see: and hear the words of Sennacherib).
The third sentence invokes Justice. Hezekiah says that the kings of Assyria have done wrong by being destructive and worshipping other gods (the kings of Assyria have destroyed the nations and their lands, And have cast their gods into the fire).
The fourth sentence requests a value. He wants to be saved out of the hand of the people who worship other gods (save thou us out of his hand, that all the kingdoms of the earth may know that thou art the LORD God). In this case, Hezekiah wants a value given to him and his people.
Notice, he didn’t tell God how to save them. He prayed a result (save thou us out of his hand). Also, Hezekiah could have prayed for a penalty to fall on Sennacherib. Instead he used Justice to request a value.
2 Kings 19:35-36 gives the result of the prayer:
It happened that night, that the angel of Yahweh went out, and struck one hundred eighty-five thousand in the camp of the Assyrians. When men arose early in the morning, behold, these were all dead bodies.
So Sennacherib king of Assyria departed, and went and returned, and lived at Nineveh.
Hezekiah didn’t specifically pray that God would strike 185,000 of the Assyrians. Hezekiah prayed he would be saved out of their hand. God did save Hezekiah out of his hand, but he did it by killing 185,000.
Pray a result and let it go. God has a plan/solution that is far superior to our plans. Besides, praying a specific punishment on others is witchcraft and God doesn’t respond to witchcraft.