What is the evidence from the Qur'an and Sunnah for the secrecy of the Dhuhr and Asr prayers and the audibility of the Fajr, Maghrib, and Isha prayers?

Allah commanded us to follow the Prophet, peace and blessings be upon him, and to emulate him in his prayer. He used to recite aloud in the Fajr prayer and in the first two rak'ahs of Maghrib and Isha, and silently in the rest. Authentic hadiths indicate that the Prophet, peace and blessings be upon him, recited aloud in prayers where recitation is audible and silently in prayers where it is inaudible. This is the consensus of Muslims. So, whoever recites aloud in a place where one should recite silently, or silently in a place where one should recite aloud, has abandoned the Sunnah (definition), but their prayer is still valid.