{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-05-06T00:09:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-05-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":59536,"title":"Integrate a Power-Tower of a Function","description":"Write a function to compute this integral: \r\n \r\nWhere the function, F(x), will be provided as an Anonymous function of x, and the value of the function between [0 : a] will always be \u003c= 1. This generalizes problem 59521 to any suitable function.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 159.774px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 79.8785px; transform-origin: 406.493px 79.8872px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10.4861px; text-align: left; transform-origin: 383.498px 10.4948px; white-space-collapse: 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\" width=\"173\" height=\"72\" style=\"width: 173px; height: 72px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 20.9896px; text-align: left; transform-origin: 383.498px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhere the function, F(x), will be provided as an Anonymous function of x, and the value of the function between [0 : a] will always be \u0026lt;= 1. This generalizes problem 59521 to any suitable function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTowerF(F,a)\r\n  I=F(a);\r\nend","test_suite":"%%\r\nF=@(x)x.^x;\r\na=[1/100,1/20,1/10,1/5,1/4,3/8,1/2,2/3,3/4,5/6,1];\r\nI=intPowerTowerF(F,a);\r\nI_correct=3.83313604;\r\nassert(isequal(round(sum(I),8),I_correct))\r\n%%\r\nF=@(x)sin(x).*cos(x);\r\na=[pi/100,pi/20,pi/10,pi/5,pi/4,pi*3/8,pi/2];\r\nI_correct=[0.00902883,0.05806967,0.13426435,0.31768753,0.41767494,0.65845847,0.83534987];\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round(I,8),I_correct))\r\n%%\r\nF=@(x)x.^3+x.^2+x;\r\na=.1:.01:.54;\r\nI_correct=7.03118292;\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round(sum(I),8),I_correct))\r\n%%\r\nF=@(x)x.^cos(x);\r\na=.01:.01:1;\r\nI_correct=[0.37993511,0.28012683,0.19681221];\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round([I(68),mean(I),std(I)],8),I_correct))\r\n%%\r\nF=@(x)sin(x).*cos(x).^x;\r\na=.01:.01:1;\r\nI_correct=25.82178819;\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round(sum(I),8),I_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-04T22:17:47.000Z","updated_at":"2026-04-16T13:54:28.000Z","published_at":"2024-01-04T22:17:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e \\\\int_0^a {F(x) ^{F(x)^{F(x)^{...}}}dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere the function, F(x), will be provided as an Anonymous function of x, and the value of the function between [0 : a] will always be \u0026lt;= 1. This generalizes problem 59521 to any suitable function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":59536,"title":"Integrate a Power-Tower of a Function","description":"Write a function to compute this integral: \r\n \r\nWhere the function, F(x), will be provided as an Anonymous function of x, and the value of the function between [0 : a] will always be \u003c= 1. This generalizes problem 59521 to any suitable function.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.44px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: none solid rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 159.774px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 406.493px 79.8785px; transform-origin: 406.493px 79.8872px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 20.9896px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 10.4861px; text-align: left; transform-origin: 383.498px 10.4948px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWrite a function to compute this integral: \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 71.8056px; border-block-end-color: rgb(60, 60, 60); border-block-start-color: rgb(60, 60, 60); border-bottom-color: rgb(60, 60, 60); border-inline-end-color: rgb(60, 60, 60); border-inline-start-color: rgb(60, 60, 60); border-left-color: rgb(60, 60, 60); border-right-color: rgb(60, 60, 60); border-top-color: rgb(60, 60, 60); caret-color: rgb(60, 60, 60); color: rgb(60, 60, 60); column-rule-color: rgb(60, 60, 60); font-family: Helvetica, Arial, sans-serif; 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\" width=\"173\" height=\"72\" style=\"width: 173px; height: 72px;\"\u003e\u003c/span\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003e \u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 41.9792px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 383.49px 20.9896px; text-align: left; transform-origin: 383.498px 20.9896px; white-space-collapse: preserve; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; \"\u003e\u003cspan style=\"\"\u003eWhere the function, F(x), will be provided as an Anonymous function of x, and the value of the function between [0 : a] will always be \u0026lt;= 1. This generalizes problem 59521 to any suitable function.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function I = intPowerTowerF(F,a)\r\n  I=F(a);\r\nend","test_suite":"%%\r\nF=@(x)x.^x;\r\na=[1/100,1/20,1/10,1/5,1/4,3/8,1/2,2/3,3/4,5/6,1];\r\nI=intPowerTowerF(F,a);\r\nI_correct=3.83313604;\r\nassert(isequal(round(sum(I),8),I_correct))\r\n%%\r\nF=@(x)sin(x).*cos(x);\r\na=[pi/100,pi/20,pi/10,pi/5,pi/4,pi*3/8,pi/2];\r\nI_correct=[0.00902883,0.05806967,0.13426435,0.31768753,0.41767494,0.65845847,0.83534987];\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round(I,8),I_correct))\r\n%%\r\nF=@(x)x.^3+x.^2+x;\r\na=.1:.01:.54;\r\nI_correct=7.03118292;\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round(sum(I),8),I_correct))\r\n%%\r\nF=@(x)x.^cos(x);\r\na=.01:.01:1;\r\nI_correct=[0.37993511,0.28012683,0.19681221];\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round([I(68),mean(I),std(I)],8),I_correct))\r\n%%\r\nF=@(x)sin(x).*cos(x).^x;\r\na=.01:.01:1;\r\nI_correct=25.82178819;\r\nI=intPowerTowerF(F,a);\r\nassert(isequal(round(sum(I),8),I_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":2,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2024-01-04T22:17:47.000Z","updated_at":"2026-04-16T13:54:28.000Z","published_at":"2024-01-04T22:17:47.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWrite a function to compute this integral: \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"heading\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:customXml w:element=\\\"equation\\\"\u003e\u003cw:customXmlPr\u003e\u003cw:attr w:name=\\\"displayStyle\\\" w:val=\\\"true\\\"/\u003e\u003c/w:customXmlPr\u003e\u003cw:r\u003e\u003cw:t\u003e \\\\int_0^a {F(x) ^{F(x)^{F(x)^{...}}}dx\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:customXml\u003e\u003cw:r\u003e\u003cw:t\u003e \u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eWhere the function, F(x), will be provided as an Anonymous function of x, and the value of the function between [0 : a] will always be \u0026lt;= 1. This generalizes problem 59521 to any suitable function.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"term":"tag:\"power 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