How to configure Coide to use DSP library for STM32f3?
INLINE is an instruction to the compiler to "inline" a function, that is, wherever it sees a function call it copies the code for the function, instead of jumping to a single copy of the code as per a normal function.

This makes the overall code size larger, in exchange for substantially quicker execution of INLINE functions (because there is no call/return overhead).

I've never used the Yagarto compiler, but my guess would be that it either doesn't support INLINE (unlikely) or that it has a different syntax (very likely).  Probably a similar story for the other errors that you're seeing.

Try using GCC instead (which does recognise INLINE, and which is probably the compiler that the ST libraries were written for); iirc there's a link to a "current build" that's easy to locate on the CooCox website.