So what is Cleopatra's story? Forgive me as I copy Wikipedia's entry on the ship:
HMS Cleopatra was a 32-gun Amazon-class fifth rate frigate of the Royal Navy. She had a long career, seeing service during the Fourth Anglo-Dutch War and the French Revolutionary and Napoleonic Wars. During the latter wars she fought two notable engagements with larger French opponents. In the first engagement she was forced to surrender, but succeeded in damaging the French ship so badly that she was captured several days later, while the Cleopatra was retaken. In the second she forced the surrender of a 40-gun frigate. After serving under several notable commanders she was broken up towards the end of the Napoleonic Wars.
Cleopatra was ordered on 13 May 1778 and was laid down on 6 July 1778 at the yards of James Martin Hillhouse, Bristol. She was launched on 26 November 1779 and had been completed by 9 September 1780. £9,202 (approximately £980 thousand at today's prices) was paid to the builder, with another £5,563.1.5d (approximately £590 thousand at today's prices) spent on dockyard expenditures. Cleopatra was commissioned in October 1779 under her first commander, Captain George Murray.
Cleopatra was initially assigned to serve with the Western squadron and was soon active in activities to suppress French cruisers and privateers. On 15 June 1780 Cleopatra and HMS Apollo captured the 26-gun Stanisland off Ostend; while the privateer Comtesse de Provence fell to Cleopatra on 11 November 1780. Cleopatra escorted a convoy to the Baltic on 1781, becoming involved in the Battle of Dogger Bank on 5 August. She passed under the command of Captain Henry Harvey in January 1783, but was paid off in April that year and fitted for ordinary at Sheerness. She remained laid up until 1790 when she began a Great Repair, and was recommissioned in January 1793 under Captain Alexander Ball.
Cleopatra continued her effective career against raiders by capturing the privateer Trois Amis on 24 March 1793 in company with HMS Lizard. She was operating from Nova Scotia from 1794, and was under Captain Charles Penrose in June 1795. He took the privateer Aurore on 3 March 1796, before passing command to Captain Charles Rowley, who coincidentally took another French ship named Aurore on 22 April that year. Rowley went on to capture the 12-gun privateer Hirondelle during his tenure, before Captain Israel Pellew took over command of the Cleopatra in September 1797. Pellew served briefly in the English Channel, taking the 16-gun privateer Emilie on 26 March 1798. He then returned the Cleopatra to Halifax in August that year. She operated off the American coasts, ranging as far as the Caribbean and Cuba, where she and HMS Andromache captured a Spanish gunboat on 22 March 1801. Pellew then returned the Cleopatra to Britain, where she spent between 1802 and 1804 under repair at Woolwich, recommissioning in July 1804 under Captain Charles Elphinstone. Elphinstone's tenure lasted less than a month, and by August Cleopatra was sailing under Captain Sir Robert Laurie.
Cleopatra spent some time in the West Indies and was homeward bound in February 1805. While sailing off Bermuda Cleopatra sighted a sail--the 40-gun French frigate Ville de Milan. She had sailed from Martinique on 28 January under Captain Jean-Marie Renaud and was bound for France with several important dispatches. Despite identifying his quarry as a superior opponent, Laurie ordered a chase. Renaud had orders to avoid combat and pressed on sail to escape Laurie. The chase covered 180 miles and lasted until the following morning, when Renaud reluctantly came about to meet the Cleopatra, which was overhauling the Ville de Milan. The engagement began in earnest at 2:30pm, and a heavy cannonade was maintained between the two frigates until 5pm, when the Cleopatra had her wheel shot away and her rudder jammed. The Ville de Milan approached from windward and ran aboard the Cleopatra, jamming her bowsprit over the quarterdeck while raking the Cleopatra's decks with musket fire. The British resisted one attempt to board, but on being unable to break free, were forced to surrender to a second boarding party. The Cleopatra had 22 killed and 36 wounded, with the loss of her foremast, mainmast and bowsprit. The Ville de Milan probably had about 30 killed and wounded, with Captain Renaud among the dead. She also lost her mainmast and mizzenmast. Three days were spent transferring a prize crew and prisoners, and patching up the ships, before the two got underway on 21 February.
However, on 23 February they were discovered by the 50-gun HMS Leander under Captain John Talbot. Leander ran up to them, whereupon they separated. Talbot chased Cleopatra, brought her to with a shot and took possession. The freed crew reported the situation to Talbot, and left him to pursue the fleeing Ville de Milan. Talbot soon overtook her and she surrendered without a fight. Both were taken back to Halifax, where the Ville de Milan was taken into service as HMS Milan, with Laurie as her captain. Laurie's engagement with the superior opponent had initially cost him his ship, but had rendered her easy prey to any other Royal Navy frigate in the vicinity. Had he not brought her to battle, the Ville de Milan could have easily outsailed the Leander or even engaged her on fairly equal terms. Instead the damage and losses incurred in breaking down the Cleopatra had left her helpless to resist.
With the loss of her captain to the command of the Milan, Cleopatra was recommissioned in July 1805 under Captain John Wright. She remained on the Halifax station, from September 1806 under Captain Robert Simpson, and from August 1808 under Captain Samuel Pechell. On 22nd January 1809 she fought an action with the 40-gun Topaze and with the support of HMS Jason and HMS Hazard captured her. Cleopatra was then present at the Invasion of Martinique in February 1809. Captain Charles Austen took command in October 1810, with command reverting to Pechell in July 1811. Captain Charles Gill took over in December 1812, followed in an acting capacity by Captain William M'Culloch in 1814.
Cleopatra was paid off in July 1814 and broken up at Deptford by 21 September 1814.
And here, for the sake of size comparison, is a nightmare scenario from the War of 1812. He would be a brave British captain indeed who would engage the USS Constellation with such a vessel. Though the Constellation is nominally a 38 gun ship, as opposed to Cleopatra's 32 guns, the differences in fire power are more significant than those numbers would imply - not to mention Constellation's advantages in hull strength. The plucky Cleopatra never engaged an American frigate, but given her record it seems many of her captains would not have shrunk from the opportunity.