Note: For v1 verbs, まい may attach to either the dictionary form or the stem (e.g., 食べるまい / 食べまい). For する, both するまい and すまい are used.
The structure ようか~まいか expresses indecision or hesitation about whether or not to do something. It conveys the speaker's internal debate – "Should I do it, or should I not?" – and is used when someone is wavering between two options.
The first part uses the volitional form of the verb (いこう行こう, たべよう食べよう, しよう), and the second part uses まい, a literary/formal negative volitional auxiliary meaning "will not" or "shall not."
Godan (V5) verbs: Volitional + か + dictionary form + まいか
Ichidan (V1) verbs: Volitional + か + dictionary form (or stem) + まいか
The verb before まい is typically in dictionary form for godan verbs and can be either dictionary form or stem for ichidan verbs. For する, both するまい and すまい are acceptable.
This pattern is commonly paired with verbs expressing indecision such as まよう迷う (to waver), なやむ悩む (to worry/agonize), and かんがえる考える (to think/consider).
The pattern has a somewhat literary or formal tone due to the use of まい. In casual conversation, speakers might instead use ~かどうか or ~か~ないか to express the same idea. However, ようか~まいか emphasizes the weight of the deliberation more strongly.