This lista is not in any particular order:
Be Myself
amor Droid
Beyond the Spectacle of the World
With Respect Lelouch
TOY
Carnival
Chocolate
Sunset amor Suicide
Blue Butterfly
Breath
Circus
Full Volume
Holography
Liberty Heart
Lie and Diamond
Naname World
Raid of Glass
Late Excuse
Aitai
Bad Apple
Bird's amor Song
Coward Mont Blanc
Emiria
Eraser
For My Soul
Happy Synthesizer (with Megurine Luka)
Killer Lady
amor is Certainly Fast
Matryoshka (with Hatsune Miku)
Mozaik Role
Mr. música (with Megurine Luka, Hatsune Miku, Kagamine Rin, Kagamine Len, and Kaai Yuki)
Panda Hero (with Megurine Luka)
Poker Face
Pray For (with Hatsune Miku and Megurine Luka)
Rosetta
Ten Faced
Ame Moyou

In my opinion, Miku is no competition for Gumi.