In the ACTS acronym for prayer, the last step is supplication. And if we are faithful in the first three steps, the last one will not degenerate into a spiritual shopping list. As we spend time in adoration, confession, and thanksgiving, our requests may change because we are aligning ourselves with the will of God.
As we see God, as we think about Him, as we begin to reexamine things, I think our prayers will being to change. Earlier we might have prayed, "Lord, those people who have done this to me, I pray you will judge them." But after we have spent time in the presence of God, we might pray, "Lord, forgive me for the wrongs that I did to them. Change my heart."
If you want to see your prayers answered more often in the affirmative, then learn to pray according to the will of God. That is the objective of effective prayer. Nothing is too big to pray about. And nothing is too small to pray about. There is a place for supplication. We don't have to feel any shame whatsoever about bringing our needs before the Lord. The Bible says, "Casting all your care upon Him, for He cares for you" (1 Peter 5:7). Bring your cares. Bring your troubles. Bring your problems.
God doesn't promise He will immediately take your problems away. But He will give you His peace in the midst of your problems.