Fukaya categories of smooth surfaces can be defined topologically, which makes them easier to compute with. Through their formal generators, topological Fukaya categories (TFC) can be related to a certain class of graded algebras, called (graded) gentle algebras. Conversely, derived categories of gentle algebras are realized as TFCs of some smooth surfaces. In this talk, I will generalize TFC construction to Z/2Z-orbifold surfaces, which introduces a new class of algebras, semi-gentle algebras. Also, we will see how to use this result to show the class of semi-gentle algebras is closed under derived equivalence. This talk is based on the joint work with Cheol-Hyun Cho and ongoing project with Severin Barmeier, Cheol-Hyun Cho, Kyungmin Rho, Sibylle Schroll, and Zhengfang Wang.