Please capitalize where necessary: after all she has done or might do, she manages to live a normal life?
A: After all she has done or might do, she manages to live a normal life?

Please capitalize where necessary: seville's bullring is one of the most handsome and important in spain, and probably the oldest (building began in 1758).
A: Seville's bullring is one of the most handsome and important in Spain, and probably the oldest (building began in 1758).

Please capitalize where necessary: the main problem in this area is to find a nonsingular algebraic variety u, that is birationally equivalent to an irreducible algebraic variety v, such that the mapping f: u v is regular but not biregular.
A: The main problem in this area is to find a nonsingular algebraic variety U, that is birationally equivalent to an irreducible algebraic variety V, such that the mapping f: U V is regular but not biregular.

Please capitalize where necessary: it is idyllically situated on the edge of the woods in a quiet and sunny loc ...
A:
It is idyllically situated on the edge of the woods in a quiet and sunny loc ...