Both Uses of

inflexible
in
The Iliad by Homer - (translated by: Pope)

So spake the imperial regent of the skies; To whom the goddess with the azure eyes: "Long since had Hector stain'd these fields with gore, Stretch'd by some Argive on his native shore: But he above, the sire of heaven, withstands, Mocks our attempts, and slights our just demands; The stubborn god, inflexible and hard, Forgets my service and deserved reward: Saved I, for this, his favourite son distress'd, By stern Eurystheus with long labours press'd?†
Book 8

inflexible = not bendable or adaptable

That iron heart, inflexibly severe; A lion, not a man, who slaughters wide, In strength of rage, and impotence of pride; Who hastes to murder with a savage joy, Invades around, and breathes but to destroy!†
Book 24 *

inflexibly = in a manner that is not bendable or adaptable

Definition:

not bendable or adaptable

in various senses, including:

not willing to compromise or make concessions -- as when a boss says "Do it my way or you're fired."
not able to adjust well to different conditions -- as of a schedule that cannot be changed
not easily bent without physical damage or injury -- as of brittle steel or person with stiff joints