Definition of "fain"

Thus Gawayne and Ector abode to gyder For syre Ector wold not awey til Gawayne were hole & the good knyȝt Galahad rode so long tyll he came that nyghte to the Castel of Carboneck & hit befelle hym thus that he was benyghted in an hermytage Soo the good man was fayne whan he sawe he was a knyght erraunt(please add an English translation of this quotation)

1485, Sir Thomas Malory, “primum”, in Le Morte Darthur, book XVII

O love, of my death my life is fain,

1883, Dante Gabriel Rossetti, A Death-Parting, line 11, Poems‎

Man and Birds are fayne of climbing high.

1591 (date written), William Shakespeare, “The Second Part of Henry the Sixt, […]”, in Mr. William Shakespeares Comedies, Histories, & Tragedies. […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, [Act II, scene i], page 125, column 2

To a busy man, temptation is fain to climb up together with his business.

1651, Jer[emy] Taylor, The Rule and Exercises of Holy Living. […], 2nd edition, London: […] Francis Ashe […]

She who would fain give the starry worlds to the object of her affection—it is a fine and beautiful pride which makes her shrink from aught of benefit from him.

1831, L[etitia] E[lizabeth] L[andon], chapter XI, in Romance and Reality. […], volume III, London: Henry Colburn and Richard Bentley, […], page 223

Leonato: I would faine know what you haue to ſay.

1598–1599 (first performance), William Shakespeare, “Much Adoe about Nothing”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, [Act III, scene v], page 113

Yet dearly I love you, and would be loved fain, But am betroth’d unto your enemy

1633, John Donne, Holly Sonnets, section XIV

The second thing I fain would have had was a tobacco-pipe, but it was impossible to me to make one…

1719 May 6 (Gregorian calendar), [Daniel Defoe], The Life and Strange Surprizing Adventures of Robinson Crusoe, […], 3rd edition, London: […] W[illiam] Taylor […], published 1719

["]Fain would I add to my beauty and my length of days if that be possible.["]

1886 October – 1887 January, H[enry] Rider Haggard, chapter XXV, in She: A History of Adventure, London: Longmans, Green, and Co., published 1887

[…] and fain would I inhale it in all its pristine fulness and vigour.

1891, George Du Maurier, Peter Ibbetson‎

Gonzalo: Now would I giue a thouſand furlongs of Sea, for an Acre of barren ground: Long heath, Browne firrs, any thing; the wills aboue be done, but I would faine dye a dry death.

1610–1611 (date written), William Shakespeare, “The Tempest”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, [Act I, scene i], page 1