Difference between Willing and Keen

WILLING vs KEEN: NOUN

The angle to which the wire tooth of card-clothing is bent between the foundation material and the point.
A loud lamentation made over the dead; a wailing.
A funeral lament sung with loud wailing
A prolonged wail for a deceased person. Cf. coranach.
A loud wailing or lament for the dead.

Ready to do something that is not (can't be expected as) a matter of course.
Spontaneous; self-moved.
Received of choice, or without reluctance; submitted to voluntarily; chosen; desired.
Free to do or to grant; having the mind inclined; not opposed in mind; not choosing to refuse; disposed; not averse; desirous; consenting; complying; ready.
Done, given, or accepted voluntarily or ungrudgingly. : voluntary.
Acting or ready to act gladly; eagerly compliant.
Disposed or inclined; prepared.
Disposed or willing to comply
Disposed or inclined toward
Not brought about by coercion or force

Having or demonstrating ability to recognize or draw fine distinctions
As physically painful as if caused by a sharp instrument
Very good
Having a fine, sharp cutting edge or point.
Having or marked by intellectual quickness and acuity. : sharp.
Acutely sensitive.
Intense or bracing.
Intense or sharp
Very penetrating and clear and sharp in operation
Having a sharp cutting edge or point
Sharp; vivid; strong.
Brave, courageous; bold, audacious.
Extremely low as to be competitive.
Marvelous.
Enthusiastic
Vehement; fierce; as, a keen appetite.
Showing a quick and ardent willingness or responsiveness, enthusiastic, eager; interested, intense.
Wonderful; delightful; marvelous.
Eager; vehement; fierce.
Piercing; penetrating; cutting; sharp; -- applied to cold, wind, etc.
Acute of mind; sharp; penetrating; having or expressing mental acuteness
Sharp; having a fine edge or point.
Bitter; piercing; acrimonious; cutting; stinging; severe.
Pungent; acrid.
Ardent; enthusiastic.
Eagerly desirous.
Great; splendid; fine.

Spontaneous, etc. See voluntary.
Synonyms Minded.
In harmony or accord; like-minded.
Characterized by promptness or readiness in action; free from reluctance, laziness, or slowness: willing horse; a willing hand.
Voluntary; cheerfully given, granted, done, or borne: as, willing service; willing poverty.
Favorably disposed; ready; inclined; desirous: as, willing to work; willing to depart.

Vehement; earnest; eager; ardent; fierce; animated by or showing strong feeling or desire: as, a keen fighter; to be keen at a bargain.
Such as to cut or penetrate easily; having a very sharp point or edge; sharp; acute: as, a keen edge.
Sharp or irritating to the body or the mind; acutely harsh or painful; biting; stinging; tingling.
Having a cutting or incisive character or effect; penetrating; vigorous; energetic; vivid; intense: as, keen eyes; a keen look; a keen rebuke; keen-witted.
Having or manifesting great mental acuteness; characterized by great quickness or penetration of thought; sharply perceptive: as, a keen logician or debater; keen insight.
Bold; daring; brave; active: applied to men.
To wail over any loss, or in anticipation of loss.
To make a loud lamentation over the dead; lament; wail.
To chap, as the hands.
Grim; fierce; savage; rapacious: applied to wild animals.
Excellent
To make keen or sharp; sharpen.

Unforced, Disposed, Lief, Volitional, Volition, Compliant, Uncoerced, Voluntary, Consenting, Fain, Glad, Amenable, Prepared, Ready, Inclined

Exquisite, Acute, Corking, Nifty, Intelligent, Incisive, Cracking, Cool, Penetrative, Intense, Sharp, Perceptive, Neat, Great, Good

Willing and able, Unforced, Disposed, Volitional, Volition, Compliant, Uncoerced, Voluntary, Consenting, Fain, Glad, Amenable, Prepared, Ready, Inclined

Exquisite, Acute, Corking, Nifty, Intelligent, Incisive, Cracking, Cool, Penetrative, Intense, Sharp, Perceptive, Neat, Great, Good

But providing as much information as possible, being willing to triage and answer questions, and being willing to test potential fixes is even better!
Market value is what someone is willing to pay that someone else is willing to sell at.
Buyer is willing to fork over and the Seller is willing to use as collateral to secure the transaction.
If you guys are willing to get me or my team to become a transcriptionist we are so willing to do so.
The price at which an asset would change hands in a transaction between a willing, informed buyer and a willing, informed seller.
The price that a willing buyer and a willing seller, both given full information, and neither under pressure to act, would agree upon.
Fair market value can be defined as the price at which an asset or service passes from a willing seller to a willing buyer.
The price for which a share could be transferred between a willing buyer and a willing seller.
Because of this, there were many market participants willing to sell credit protection but few willing to purchase it.
The price that a willing buyer and a willing seller would agree to.

Senate was not keen to investigate these matters.
Young Keen gave no explanation for the shooting.
Management always keep a keen eye on everyone.
Do you have a keen knowledge of mortgages.
APRA is keen to see new entrants succeed.
But he was now becoming a keen partisan.
Really keen to get back into it though.
Walden Robert Ealey Robert Earl Keen Robert Earl Keen, Jr.
Most recruiters are just as keen to have square pegs in square holes as you are keen to find the right job for you.
Keen to resume flights to Karachi cheap tickets with Kuwait Airways is keen to its.