Looking for a competition (sports, music, etc) manga where the female lead is skilled at what she does. Also, where she isn't sexualized either.

For example:
-Smash!
-Girl got game/Power!!
-Benjiiro Hero
-Matsuri Special
-Over Rev!
-Teppu
(I haven't read a some of these so correct me if they don't fit)

NOT looking for stuff like:
-Nononono (she's sexualized)
-Uwasa no Midori-Kun (also sexualized)
-Classi9 (she is not good at music and has to learn from her classmates)
-La Corda d'Oro (she's only good because of the magic violin, if I remember correctly)

Romance isn't important, I don't care if there is or isn't any. It'd be best if she was also mentally strong and not a wallflower.

Kono Oto Tomare!
Baby Steps
Butter!!!
I-Revo
Green Boy: Shouting to You
Saotome Girl, Hitakakusu

"The world is a dangerous place to live, not because of the people who are evil, but because of the people who don't do anything about it." - Albert Einstein

Hm, you could try Saotome Senshu, Hitakakusu.

EDIT: Ah, princess bubblegum beat me to it.

Yes, you're worthy!

Asahinagu
BaggataWay
Bamora!
Bushidou Sixteen
Hanakaku - The Last Girl Standing
Hanebado!
Kenrantaru Grande Scène
Nanamaru Sanbatsu maybe (the female lead is a secondary protagonist)

I also love Baby Steps, but the male lead is the main focus.

Shoujo Fight
Chihayafuru

Series where the MC is male, but the main female character fits your request:
Takkoku!!!
Buyuden
Rough
Katsu!

Hybrid Berry