My windsheild wiper is broken, A mechanic told me I would have to replace the wiper transmission.

Wiper transmission? Or more likely the wiper motor?
Parts and labor prices vary significantly from one area to another so use this as a guide not as fact:
You could maybe find that motor for $50-60 or as high as $130+, depending on new or rebuilt, warranty or no warranty.
As far as labor: Expect somewhere around two hours labor plus or minus to do the diagnosis and do the install.
2.0 X (shop labor rate)
+
(Price of part)
=_________
Final cost to have your wipers working as normal... $??
What is your mechanic quoting you for that job?