Hence such verb-phrases with will in the first person are not forms of the future tense. They are special verb-phrases expressing willingness or desire.

235. In the first person shall, not will, is the auxiliary of the future tense in both assertions and questions. It denotes simple futurity, without expressing willingness, desire, or determination.

Will in the first person is used in promising, threatening, consenting, and expressing resolution. It never denotes simple futurity.

I. Simple Futurity (Future Tense)
II. Promises, Threats, etc.

I’ll and we’ll are contractions of I will and we will and can never stand for I shall and we shall.

236. When willingness is expressed by an adjective, I shall is correct; when by an adverb, I will. Thus,—