ἄν is best described as the Conditional Marker in Greek.
It is usually but not always translated as would or should.
Here are some prose samples
From Plato's Apology the iterative
Διηρώτων ἄν αὐτοὺς τί λέγοιεν I often asked them what they meant.
Ἄν From Demosthenes 3.27
ἄλλα σιωπῶ, πόλλ̕ ἂν ἔχων εἰπεῖν but I am silent though/ I would have / having much to say
ἄν with Subjunctive ὅπου ἂν ὦ Wherever I may be .
Ἄν in a Compounds becomes Whenever ἐάν ἐπειδάν ὅταν
ἐάν κελεύῃ πειθόμεθα when if ever he orders we obey
ἐάν ἔλθη νικήσομεν whenever he comes we (will) win
A set showing εἰ and ἄν in IF A THEN B statements
εἰ ταῦτα ἐγίγνετο ἀπέθνῃσκεν ἄν if this was happening he would be dying
εἰ ταῦτα ἐγένετο ἀπέθανεν ἄν if this had happened he would have died
εἰ ταῦτα ἐγένοιτο ἀποθάνοι ἄν if this should happen he would die
Indirect ἔφη εἰ ταῦτα ἐγένετο ἀποθανεῖν ἄν