What must a girl do who reached puberty at the age of ten, did not tell anyone, and broke her fast on some days of Ramadan due to her ignorance of the ruling, knowing that she does not remember the number of days she broke her fast?

The questioner must make up the days she missed in Ramadan after reaching puberty. Ignorance does not waive the obligation to make up the fasts; it only removes the sin. There is no expiation required for delaying the make-up fasts if the delay was due to an excuse or ignorance. A Muslim must learn the individual obligations.