Keyboard embedded calculator

Math/Script Keyboard includes an integrated scientific calculator that doesn't have its own input or output interface. Instead, it can be linked to any input method. This means that any text editor or input field (such as Google search) can serve as a calculator. The intended purpose is to enable typing and calculation simultaneously without the need for retyping, while also retaining the results. Calculation results are automatically inserted by pressing ≛, displaying as [=xxxx] or [✔]. 

123+456[=579.0] (calculation)

a₁=5[✓] (variable definition)

b₂=6[✓]

a₁+b₂[=11.0]

gas 50+35+76[=161.0] (1st non calculable removed and can be used as  a comment)

f(x)=x²-3x+5*sin(x)[✓] (function definition)

f(5)[=10.43577871373829] (function calculation)

(recursive function calculation for Fibonacci sequence)

clear()[✓] (clears internal memory)

f(1)=1[✓](initial value)

f(2)=1[✓] (2nd initial value)

f(n)=f(n-1)+f(n-2)[✓] (recursive definition, sum of 2 prior values)

f(3)[=2.0] (calculation results,  1+1)

f(10)[=55.0]

f(100)[=3.54224848179262E20]

f(1000)[=4.346655768693743E208] (The calculator's recursive engine has built-in memorization capability and extends beyond pure recursive functions. ) 

f(1500)[=Infinity] (answers are too big to display)

This calculator does not have loop capability, like for or while.  However, iterative calculation can be converted to recursive calculation.

1. 1+2+3+4+5+....100=?

clear()[✓]

f(1)=1[✓] (initial value)

f(n)=n+f(n-1)[✓] (recursive definition, current number + prior value)

f(100)[=5050.0] (result)

2. 1²+2²+3³+4²+...100²=?

clear()[✓]

f(1)=1[✓]

f(n)=n²+f(n-1)[✓] (recursive definition current value square + prior value)

f(100)[=338350.0] (results)

3. 1*2*3*4*...n=? (This is a readily available factorial function used solely for recursive function demonstration purposes.)

clear()[✓]

f(1)=1[✓]

f(n)=n*f(n-1)[✓] (recursive definition, current value*prior value)

f(5)[=120.0]

f(100)[=9.33262154439441E157]

Rule for comment separation

1. split with  delimiters of ';',':','\t','\n','@','#','$','&','~','?' and pick last element and calculate.

2. If there's an error, split based on the maximum consecutive spaces and try again.

1+2+3

group A   4+5+6[=15.0] (First, attempt to calculate 'group A 4+5+6'. If there's an error, split the expression again based on the maximum number of spaces and select the last portion '= 4+5+6'. The answer would be 15.)

3. + sign can be skipped as shown below:

aaa       1  2  3[=6.0] (split to '1 2 3' and add missing signs to get '1+2+3', resulting in an answer of 6.)

List of available functions and usage.

sin(45)[=0.7071067811865469]  (angle is based on degree)

cos(60)[=0.5]

tan(60)[=1.7320508075688732]

asin(0.5)[=30.0] (inverse sign)

sin(30)[=0.5]

acos(0.5)[=60.0]

atan(3¹ᐟ²)[=60.0]

sinh(1)[=1.1752011936438014] (hyperbolic sine)

(e-e⁻¹)/2[=1.175201193643804]

cosh(1)[=1.5430806348152437]

tanh(2)[=0.9640275800758169]

asinh(0.1)[=0.09983407889920758] (inverse hyperbolic sine)

acosh(5)[=2.2924316695611777]

atanh(0.5)[=0.5493061443340549]

abs(-3)[=3.0]

log(2)[=0.3010299956639812]

log(2,2)[=1.0] 

ln(2)[=0.6931471805599453]

rand(5)[=0.9160358476265523] (random number between 0 and 5)

factorial(5)[=120.0]

!(5)[=120]  (conflict with the separator at this point, but it will be resolved in the next update.)

round(1.6)[=2.0] (round to the nearest integer)

round(-1.6)=[-2.0]

sqrt(2)[=1.4142135623730951]

√(2)[=1.4142135623730951]

∛(2)[=1.2599210498948732] (cubic root)

2⁽¹ᐟ³⁾[=1.2599210498948732]

exp(1)[=2.71828182845905]

exp(2)[=7.389056098930676]

e²[=7.389056098930676]

e[=2.71828182845905] (built-in constant)

π[=3.14159265358979] (built-in constant)

pi[=3.14159265358979] (built-in constant)

C(5,2)[=10.0] (combination, ₅C₂)

P(5,2)[=20.0] (permutation, ₅P₂)