What is the ruling on taking a Mushaf from a carton that collects abandoned Mus-hafs in school, and is that considered theft, and what should be done to atone for this act?

If the aforementioned Mushaf (copy of the Qur'an) is owned by one of the students, then taking it without the owner's permission is wrong, and its expiation is to return it to its owner. If that is not possible, then give it away as charity by placing it in a mosque or an Islamic center. This act is not considered theft, but rather a betrayal and an encroachment upon another's property. However, if the evidence indicates that students leave their Mushafs because they no longer need them and allow anyone to take them, then there is no sin upon you for taking it and keeping it.