Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
† 1. maia, ae, f., = μαῖα, a large kind of crab, Plin. 9, 31, 51, § 97; al. maea.
2. Māia, Māja (written by Cicero Majja, like ejjus, pejjus, etc.; v. the letter J), ae, f., = Μαῖα.
Māius, i, m. [Maia], usually mensis Maius, the month of May: Cincius mensem (Maium nominatum putat a Maia, quam Vulcani dicit uxorem, Macr. S. 1, 12, 18: (mensis) tertius a majoribus Maius, Varr. L. L. 6, 4, 34; Cic. Phil. 2, 39, 100; Ov. F. 5, 490; also simply Maius, Ov. F. 5, 185.
As adj.: Kalendae Maiae, Cic. Fam. 4, 2, 1; Ov. F. 4, 947: Idus Maiae, Cic. Att. 3, 8, 2; Prop. 4 (5), 5, 36.
mājus, a, um, adj. [root mag, whence magis, magnus], an old word for magnus, great, e. g. Majus Deus, i. e. Jupiter: Dea Maia, Macr. S. 1, 12, 17.