Queen and pawn against queen is usually a draw if you defend well. The simplest draw is your king in front of the pawn. When your king is too far away, keep checking, so the pawn never gets time to move. Against a knight or rook pawn, the corner far from the queening square is a safe place for your king.
Every move is checked with an endgame tablebase, which knows the exact result of every position with up to seven pieces. The computer defends perfectly, and if a move throws the result away, the trainer stops and shows you a better one.
