愿(yuàn) - to be willing, to wish, may it be that in Mandarin

愿 (yuàn) covers two related ideas: being willing to do something, and wishing that something were so. As a single character it is on the formal and literary side, and in ordinary speech the two syllable forms do most of the work: 愿意 for willingness, 愿望 for a wish, 心愿 for a heartfelt hope.

Where the bare character still thrives is at the front of a good wish. 愿你一切顺利, 愿他安息, 但愿如此 are all completely current, and they are how Chinese does may you and I do hope. 但愿 in particular is worth memorising as a chunk.

The trap is treating 愿 as an ordinary want. For everyday wanting, use 想 or 要. 愿 implies consent or a solemn hope: 我愿意 is what you say at a wedding, not what you say at a noodle stall.