1.Prepositional phraseAt any rate: anyhow, regardless (emphasizing that a point doesn't matter or hardly matters).
"The product is duly prohibited by law, but in any event, it is still available on the black market."
2.Prepositional phraseAt any rate: by any measure, any way one slices it, in every case, no matter what (emphasizing that a point matters so much that there is no case in which it does not matter).
"You can grumble all you like, but in any event, you'd better be there at the appointed time."
3.Prepositional phraseUsed other than figuratively or idiomatically: see in, any, event.
"Kinetics might be described as a series of events, and in any event, there is some instant at which some change begins."