val x: (suspend (Int) -> Int) = suspend { x: Int -> x * x }

even when specifying all the types explicitly i get this error:

Type mismatch.
Required: suspend (Int) → Int
Found: suspend () → Int

why?

because this is the signature of suspend itself:

public inline fun <R> suspend(noinline block: suspend () -> R): suspend () -> R = block

thus it cant accept any function with an input

how do i fix my code then ?

val x: suspend (Int)->Int) = { x:Int -> x*x }

depends on what you want, if you just mean a lambda (Int) -> Int, then simply

val x = { x: Int -> x * x }

would be enough

thanks