All prayers a mixture of faith and error

Calvin's Institutes (1559)
Book 3 of 4 - How We Receive the Grace of Christ

Chapter 20 - Prayer as exercise of faith and way we receive God's benefits

Sections 15-16 - God even hears defective prayers

15. Examples: Judges 9:20; 16:28; Ps 107:6, 13, 19; 1 Kings 21:29. He does this to emphasize His mercy. Ps 106:13, 43; Judg 3:9; Matt 5:45. Sometimes saints in Scripture prayed without God's promise - Gen 18:23 - or even against His command - 1 Sam 15:11; Jer 32:16. "They pray according to His will, not that hidden and unchangeable will but the will that He inspires in them." In such a case, "we must ask of God conditionally." See Ps 7:6. The "prayers of the saints.... are a mixture of faith and error."

16. God answers our prayer only by constantly forgiving the error and irreverent emotions with which our prayers are mixed. David's Psalms have this! Ps 39:13. These should be repudiated [!], but God quickly forgives as we confess. We lift our hands in prayer to agree our hearts should be lifted up to God, though they "stay on the ground." We must confess our sins, how little we feel the weight of our sins, and how few of our sins we are aware of. Our prayers are often tinged with questions in trial - Ps 80:4; Lam 3:8. These are defects of faith, but forgiven as we remain humble and reverent before God.