[verb (volitional)] + か + [verb (dictionary form)] + まいか [v1] [verb (volitional)] + か + [verb ます-stem] + まいか [する] しようか + するまいか / すまいか
ようか~まいか says you can't decide whether to do something: "whether or not to". The same verb appears twice, first in the volitional form with か, then in the dictionary form with まいか. A verb of hesitation such as まよう迷う, なやむ悩む or かんがえる考える usually follows.
The second half takes the dictionary form, not the volitional and not the ない-form.
A る-verb can also put the ます-stem before まい (たべ食べまいか), and する has すまいか beside するまいか.
まい is a written, formal negative, so the pattern belongs in writing and careful speech. In conversation, say ~か~ないか, or repeat the verb with どうしよう.