Alan FitzFlaad, (Fitz = Fils = son) Dapifer (Steward) of Dol in Brittany near the Mont St Michel came to England with William the Conqueror and settled in Sporrel in Shropshire. I believe that this Sporrel is the origin of the Sproule name.
Alan Fitzflaad was the father of Walter FitzAlan who became the first High Steward of Scotland when King David Iof Scotland made his acquaintance at the court of King Henry 1 of England.
His son was Alan FitzWalter 2nd High Steward
His son was Walter FitzAlan 3rd High Steward of Cowden Hall whose daughter, Elizabeth Spruell, married Malcolm, Earl of Lennox.
His son was Alexander, 4th High Steward.
His son was James 5th High Steward and is considered to be the common ancestor of the Sproules of Renfrewshire.
His son was Walter Stewart 6th High Steward who married Marjorie Bruce daughter of Robert the Bruce. Their son became Robert II of Scotland, First of the Stewart/Stuart dynasty.
The name Stewart was probably just a clerical error from Steward when surnames first began to be used. When Mary Queen of Scots married the French Dauphin (heir to the throne) there was no "W" in the French language and so Stewart became Stuart.