What is the definition of shirk that God does not forgive, with contemporary examples of it, and is it a matter of belief, or does it include actions and words? And does one whose intention in an action is not for the sake of God commit a sin, and is one rewarded for doing good without recalling the intention?

Shirk (polytheism/idolatry) is dangerous and grave. Ibn al-Qayyim and al-Sa'di defined it as being of two types: major and minor. The major shirk is not forgiven by Allah unless one repents from it. It is when a person takes a rival to Allah in love, veneration, and worship. Examples of major shirk in the modern era include: ruling by man-made laws that contravene Islamic Sharia, and adhering to atheistic ideologies such as communism and secularism. Shirk does not occur by belief alone; rather, it encompasses utterance, intention, and belief.