there's more rape of notations in this than rapeseed.

first of all, note the ambiguous use of the brackets. The curly bracket is used as the delimiter for formal parameter of a function and also as delimiter for formal parameter of a expression. The round bracket is also used as delimiter for formal parameter of a function.

then, notice that this definition tries to do several things:

- definition of Laplace transform
- show notational equivalence
- mixed nonsensical use of equal sign and define sign. ① the equal sign is used for definition of notational equivalence. ② The left side of the definition is a equation. It seems to define a equation by a integral. ③ lastly, the integral notation is all eff'd up with that “dt” thing. There's no variable named d here.
- illogical and extraneous use of variables. Here, there's a confusing change of variable from “t” to “s”, even though we are defining a function of one variable, there's no need to mention its formal parameter.

in general, mathematicians use math notations like a diagram of pictographs, the same way children draw pictures to express meaning. The output thereof, is not grammatically coherent. We understand them by years of convention and context and guess-work.

y'know? sometimes we send a piece of math on paper in spaceship to outer space in hope that aliens who see it might appreciate our intelligence. The aliens would probably go “WTF ambigram❓”.

better:

ℒ[f[x]][s] := ∫[ ⅇ^(-s*t) * f[x],{x,0,∞}]