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[insert Arc joke here]

Didn't you mean (insert Arc joke here) ?

Doesn't matter. In Racket you can use either bracket-style, as you please.

I thought () was used for function applications and [] for those that weren't. For example (let [x 3] ... )

Nope they are interchangeable.

The compiler may not mind, but isn't that what they are actually used for?

Not quite; in (let ([x 1] [y 2]) (+ x y)) there's a set of parens which aren't used for function (or macro) application.

In Arc, square brackets are shorthand for an anonymous function. The argument is an underscore. ([+ _ 2] 2) returns 4.