May(verb) also means can, will, be-allowed, be-able or to-have-permission.
Etymology of may (verb)
From Middle English mowen, mayen, moȝen, maȝen.
From Old English magan, *mugan.
From Proto-West Germanic *magan
From Proto-Germanic *maganą,
From Proto-Indo-European *megʰ-.
It is cognate with Dutch mag (“may”, first and third-person singular of mogen (“to be able to, be allowed to, may”))
Information from WikiDictionary.
May is interchangeable with will, can, be able to, have permission to.
According to WikiDictionary:
(obsolete, auxiliary) To be able; can. [8th–17th c.]
1624, Democritus Junior [pseudonym; Robert Burton], The Anatomy of Melancholy: […], 2nd edition, Oxford, Oxfordshire: Printed by John Lichfield and James Short, for Henry Cripps, OCLC 54573970, partition II, section 3, member 6:
But many times […] we give way to passions we may resist and will not.
(intransitive, poetic) To be able to go. [from 9th c.] quotations
Example: 1600, William Shakespeare, A Midsummer Night's Dream, III.3:
O weary night, O long and tedious night,
Abate thy houres, shine comforts from the East,
That I may backe to Athens by day-light […].
(modal, defective, auxiliary) To have permission to, to be allowed to. Used in granting permission and in questions to make polite requests; takes a simple bare infinitive. [from 9th c.]
Example:you may smoke outside; may I sit there?
Synonyms: can, could, might
The verb may is sometimes interchangeable with can as per Merriam Webster:
May (auxiliary verb)
The verb may is interchangeable with will as per Britannica.com:
May (formal + old-
used to indicate the reason for something or the purpose of something
Examples:We exercise so that we may [=will] be strong and healthy. [=we exercise in order to be strong and healthy]
I work hard so that my family may [=will] not go hungry.
So it's highly possible that in (22:77)
O you who have believed, bow and prostrate and worship your Lord and do good - that you may succeed.
The may is used there means will, can, be able or have permission to.
So (22:77) would mean
O you who have believed, bow and prostrate and worship your Lord and do good - that you may [=will/can] succeed.