@Rouben Rostamian  Upon carefully rereading the Question, I think that your suggestion fulfills the OP's intention. I at first thought that they wanted to integrate the right side and maintain it as an equation with the same left side, which is what my code does.

@vv Nothing has been deleted. If you click on it from the main menus, you may see Page Not Found. This is just a bug in MaplePrimes. If instead you go to the "Active Conversations" page, then click on it, you will see it. It seems to take MaplePrimes somewhere between 1 and 2 hours to re-index the main menu links. After that, it'll appear as normally.

@vv Although it wasn't I who branched this off from its former parent Question, I think that it was the right decision to do so:

• It's an explicit mathematical question.
• Maple can help with its solution.
• An elaborate Answer using Maple has been posted.

@Rouben Rostamian To do that, you'd need to implement the arithmetic operations multiplication, addition, and greater than in Logic. It would be quite elaborate, but in theory doable^[*1]. If a problem can be solved with ordinary arithmetic, it'd probably be best to avoid using Logic.

Note that the only arithmetic operations needed for Joe's solution are less than, add 1, and subtract 1.

^[*1]as shown with great detail, precision, and fanfare in Whitehead and Russell's Principia Mathematica, 1913.

@q41b3 You're welcome. I don't know if it's worth studying your book for its Maple content due to the age. Perhaps only the math content is relevant anymore. There's been a lot added to Maple since 2002, including the packages LinearAlgebra, Statistics, and Finance (which handles the main stochastic differential equations used in finance).

I've extensively updated this code with comments and to use syntax features new to Maple 2019. In particular, I like the new local syntax, which allows placement of the declaration close to where the variable is used, which I think is more robust and easier to read. I've also used the new increment syntax, ++var, and the new neutral-operator syntax, which allows the use of the operator in functional form (i.e., coming before it arguments) without the use of back quotes.

I recently encountered on MaplePrimes a problem for which Fisher's exact test is ideal, and I've included that problem.

Since MaplePrimes doesn't reproduce Code Edit Regions, here's my code, and the worksheet follows.

#This code uses features new to Maple 2019.

ContingencyTableTests:= proc(
	O::Matrix(nonnegint), #contingency table of observed counts 
	{method::identical(Pearson, Yates, G, Fisher, Fisher[count]):= 'Pearson'}
	#Use 'method' = 'Fisher[count]' to count how many table variations are 
	#needed for Fisher's.
)
description 
	"Returns p-value for Pearson's (w/ or w/o Yates's continuity correction)" 
	" or G chi-squared or Fisher's exact test."
	" All computations are done in exact arithmetic."
;
option
	author= "Carl Love <carl.j.love@gmail.com>, 29-May-2019",
	references= (                                                           #Ref #s:
		"https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test",         #*1
		"https://en.wikipedia.org/wiki/Yates%27s_correction_for_continuity",  #*2
		"https://en.wikipedia.org/wiki/G-test",                               #*3
		"https://en.wikipedia.org/wiki/Fisher%27s_exact_test",                #*4
		"Eric W Weisstein \"Fisher's Exact Test\" _MathWorld_"
		"--A Wolfram web resource:"
		"   http://mathworld.wolfram.com/FishersExactTest.html"               #*5
	)
;
uses AT= ArrayTools, St= Statistics, It= Iterator;
local
	C:= AT:-AddAlongDimension(O,1), R:= AT:-AddAlongDimension(O,2), #column & row sums
	c:= numelems(C), r:= numelems(R), #counts of columns & rows
	n:= add(R), #number of observations

	#All remaining code in `local` applies strictly to Fisher's.
	`&*!`:= mul@factorial~, 
	Cutoff:= &*!(O), #cut-off value for less-likely matrices
	CTs:= 0, #count of contingency tables with same row and column sums as O.
	Devs:= 0, #count of those tables with probabilities <= that of O.
	
	#Generate recursively all contingency tables whose row and column sums match O.
	#A very similar recursion is documented on the Maple help page
	# ?Iterator,BoundedComposition as example "Contingency Table".	
        CountCTs:= proc(C, i)
	local X; 
		`if`(i=r, 1, add(thisproc(C-X,i+1), X= It:-BoundedComposition(C,R[i])))
	end proc,
		
        #Using the same recursion as above, generate the tables and compute their  
	#probabilities under the null hypothesis. The formula for the probability is
	#from reference *5. Sum probabilities of all those at least as improbable as O. 
	#Parameters: 
	#   C = column sums remaining to be filled; 
	#   F = product of factorials of entries of contingency table being built;
	#   i = row to be chosen this iteration
	AllCTs:= (C, F, i)->
		if i = r then #Recursion ends.
			if irem(++CTs, 10^5) = 0 then Report() fi;
			#Last row is C, the unused portion of column sums:
			if (local P:= F*&*!(C)) >= Cutoff then ++Devs; 1/P else 0 fi
		else
			local X;
			add(thisproc(C-X, F*&*!(X), i+1), X= It:-BoundedComposition(C,R[i]))
		fi,
   
	Report:= ()-> userinfo(
		1, ContingencyTableTests, NoName, CTs, "tables evaluated, of which", Devs, 
		"are at least as improbable as the observed input."
	)     
;
	if method in {'Fisher', 'Fisher'['count']} then
		if method = 'Fisher'['count'] then return CountCTs(C,1) fi; 
		local p:= AllCTs(C, 1, 1)*&*!(R)*&*!(C)/n!;  #p-value (see *5)
		Report();
		p
	#Readers only interested in Fisher's exact test can ignore everything below
	#this point.
        else #Use one of the chi-squared methods: Pearson, G, Yates.
		local E::rtable; #matrix of expected values under null hypothesis 		
		try
			E:= rtable(
				(1..r, 1..c), 
				(i,j)-> R[i]*C[j]/n,
				#The chi-squared tests aren't sufficiently
				#accurate if any cell has expected value < 5:
				datatype= satisfies(x-> x >= 5) 
			)
		catch "unable to store":
			error
				"cell expected value too small for chosen method;"
				" use 'method'= 'Fisher'"
		end try;
		userinfo(
			1, ContingencyTableTests, 
			"Table of expected values under null hypothesis:", 
			print(
				`if`(
					E::'rtable'(posint), 
					E, 
					E=subsindets(E, Not(integer), evalf[1+ilog10(n)])
				)
      		)
		);
		#Pearson's, Yates's, and G all use a chi-square statistic,
		#each computed by a slightly different formula:
		local Chi2:= add@~table([
			'Pearson'= ((O,E)-> (O-E)^~2 /~ E),                     #see *1
			'Yates'= ((O,E)-> (abs~(O-E) -~ 1/2)^~2 /~ E),          #see *2
			'G'= ((O,E)-> 2*O*~map(x-> `if`(x=0, 0, ln(x)), O/~E))  #see *3
		]);
		1 - St:-CDF(ChiSquare((r-1)*(c-1)), Chi2[method](O,E)) #p-value 
	fi   
end proc:

Download FishersExact.mw

@q41b3 Well, you can still choose this Answer as best.

@q41b3 The difference between else if and elif is purely syntactic. Each if must have a corresponding terminator (fi, end if, or end---those three being equivalent in this context). Using else if starts a new if statement, so it requires two terminators. 

@melika mokhtari Your z contains the derivative to the 6th power.  Then c contains a term with z in the denominator. Then ode contains separate terms with c and the derivative squared.

I don't know how to fix it.

@tomleslie Yes, I agree that if the OP is working with mathematical structures that are represented symbolically in Maple (rather than working with strings), then it is far better to use the built-in type system than regular expressions. 

If the OP gives more details of their project, I'd be happy to show some examples of using types.

@torabi You need to change F[n] to F[.., n]. The former is a row vector, and the latter is a column vector.

@tomleslie As I said last night, our relative memory and cputime numbers were not surprising.

I just wrote a version that uses a full-size Array, as yours does. My memory usage is still much lower than yours, which I find surprising, and also my cputime is much lower. 

CodeTools:-Usage(sieve(2^24)): #Tom's procedure, not copied here.
memory used=1.37GiB, alloc change=-329.75MiB, cpu time=9.72s, real time=6.10s, gc time=4.28s

restart:

EratosthenesSieve:= proc(N::posint)
description "Returns list of primes <= N";
   if N < 5 then return remove(`>`, [2, 3], N) fi;
   local p, P:= rtable(2..N, k-> k);
   P[[seq(4..N, 2), seq(seq(p^2..N, 2*p), p= thisproc(isqrt(N))[2..])]]:= ();
   [seq(P)]
end proc 
:
CodeTools:-Usage(EratosthenesSieve(2^24)):
memory used=0.90GiB, alloc change=102.38MiB, cpu time=4.94s, real time=3.16s, gc time=2.05s

I post this not out of any desire to criticize, but simply in the spirit of education and good-natured sportsmanship.

@torabi So, do you not understand the meaning of the error message? Are you incapable of tracking it down yourself? You've been posting on MaplePrimes for nearly 4 years. I can understand your need for some help with the details of a Matlab-to-Maple translation, but I can't hold your hand for every step.

Second degree? Ha! Just eyeballing it, I see that it's at least degree 8 in the derivative.

@torabi You need to replace exp with LinearAlgebra:-MatrixExponential.