Final answer:
Apollo did not trade his herdsman staff with Hermes; rather, Hermes traded the lyre he invented to receive Apollo's forgiveness for stealing his cattle.
Step-by-step explanation:
The mythological trade between Apollo and Hermes is an intriguing tale from Greek mythology. There is no direct reference to Apollo trading his herdsman staff specifically with Hermes in the classical sources readily available up to my knowledge cutoff date in 2023. However, the story of Hermes and Apollo typically involves Hermes trading the lyre he invented for Apollo's forgiveness, as Hermes had stolen Apollo's cattle on the day of his birth. This tale underscores the cunning and conniving nature of Hermes as well as his capacity for making deals and his association with boundaries and exchanges.