Before I offer you evidence, I wish to clarify that prayer is submission to God, and being sensitive to Him, so I do and say what He pleases . . . what He has me asking and seeking. So, this is what I mean by prayer . . . not only asking God for things, but personally submitting to Him so He and I are in personal sharing and communication in His love, then see what He has me praying for, in His personal guiding of what I say in prayer
"for it is God who works in you both to will and to do for His good pleasure." (Philippians 2:13)
So, I understand from this scripture, that God in us works in our willing and doing to have us praying the way He desires, asking what He has us ask

In His Spirit we do the praying He has us doing. And in Romans 8:26 our Apostle Paul says >
"the Spirit Himself makes intercession for us, with groanings which cannot be uttered."
So, the Holy Spirit is praying for us . . . not only with talk and words, but "with groanings which cannot be uttered."
So, prayer, I consider from this, includes deeper-than-words groaning of love and affection and appreciation for God, and groaning of appreciation and affection for one another, and groaning of compassion for any and all people > in love's prayer.
Now, can I give you evidence that I really am in such blessed personal communication with God during prayer?
I can offer my testimony. In a court, evidence includes the testimony of witnesses. But can you really prove each witness is telling the truth, if all you have is say-so? no
So, in case you accept personal testimony as being evidence, then I offer my personal experience that I do experience God in very kind and sweet and humble and gentle and soul-resting and soul-soothing love sharing with me and guiding me in prayer. And this matches with what I find in the Bible >
Jesus is "gentle and lowly in heart" > Matthew 11:29 > "and you will find rest for your souls." And I do experience that in His love and personal guiding He is gentle and humble with me in feelings and emotions of His love, and He does give me rest for my soul, in spite of myself and people and things in my life. He is better and sweeter and kinder and does me more good than any human pleasure stuff. This is my testimony, in case you consider personal testimony to be evidence. Plus, also in the Bible, we have >
"praying in the Holy Spirit, keep yourselves in the love of God" > in Jude 20-21 > this is directed, in the Bible, showing me that the writer knows that prayer is not only talking into the air, but prayer is a process of keeping ourselves in God's own love . . . so prayer is relating personally with God and personally submitting to how He keeps us and guides us in His love
So, my personal experience matches with certain things I have discovered in the Bible

It appears that certain writers, thousands of years ago, have experienced what I am discovering with God, about prayer.
There is relating, in His love > Romans 5:5 is clear how God does share His very own love with us, right "in our hearts". So, if God so greater and superior is so personally sharing, surely God is not conceited.
Well, as you can see from what I have offered, above, and from Bible quotes > that is not all there is to prayer. But yes we do ask for things, and we do get no for an answer. But I keep discovering how things that do come are included in loving and caring for people.
So, God is in love evaluating each prayer, and answering with love benefits; but because God is all-loving, how He answers fits together with how He is loving and doing good to others, also; with His answers can come more and more family loving and sharing and caring with others. Therefore, I have needed much correction (Hebrews 12:4-11, James 5:16), first, so I can be ready for things I have asked for.