How did each of the new religions in the classical age (ex. Buddhism, Confucianism, Islam) play a role in their culture of their regions?

Each of these three religions became the ruling ideology
of an empire in the ancient world.

Buddhism was founded by
Siddhartha Gautama (483-563 BCE) on principles of nonattachment and nonviolence.
Grasping for things is the cause of suffering in life, and giving up attachments leads
to joy and freedom. When the Emperor Ashoka (304-232 BCE) completed his conquests of
north India, he turned to Buddhism to help rule the empire. He spread Buddhism and in
particular, promoted the ethical virtues of compassion and nonviolence throughout the
lands he ruled.

Muhammad (570-632 CE) was the founder of
Islam, based on the revelations from God he received that became known as the Quran. He
taught that all Muslims should submit to the will of God and that people had a duty to
develop a just society on earth. He also taught tolerance for the Jews and Christians
under Muslim rule. In the centuries that followed, the Islamic empires ruled based on
these principles of valuing special justice and tolerance for the other monotheistic
religions in their territories.  These empires were the early Caliphate (from the death
of Muhammad until 661 CE), the Umayyad dynasty (661-750), and the Abbasid (750-1258)
dynasty. These ruled throughout the Middle East and parts of Europe, Asia, and
Africa.

Confucianism was based on the ethical teachings of
the figure we call Confucius (551-479 BCE). He taught a system in which one should
strive to find their inner humanity or empathy. From that proper social conduct would
follow. Also, he taught the importance of education and respect for parents, elders, and
superiors, which created a hierarchical system in society. Later, the Han dynasty of
China (206 BCE-220 CE) and following dynasties adopted Confucian principles in their
rule. Later dynasties also began administering exams based on Confucian teachings. Doing
well on exams led to key government posts.